Phosphate and borate glasses with high elastic moduli

ABSTRACT

Glass compositions with high Young&#39;s modulus are disclosed. The glass compositions may include phosphorus oxide (P2O5), alumina (Al2O3), boron oxide (B2O3), lithium oxide (Li2O), magnesia (MgO), titania (TiO2), lanthanum oxide (La2O3) and other components.

This application claims the benefit of priority to Dutch PatentApplication No. 2030887 filed on Feb. 10, 2022, which claims priorityfrom U.S. Provisional patent application Ser. No. 63/300,724 filed onJan. 19, 2022, the content of which is relied upon and incorporatedherein by reference in its entirety.

FIELD

The present disclosure generally relates to phosphate and borate glasseshaving high elastic moduli and low optical dispersion.

BACKGROUND

Glass is used in a variety of devices and constructions, including, inparticular, optical (e.g. laser) and electronic devices. Also, glass canbe used as a substrate or a carrier for articles (e.g. wafers,electronic devices) during processing or fabrication, including exposureof the articles to aggressive media, such as alkalis, acids, oxidizers,etc.

The required properties of glass depend on the specific application andprocessing conditions. However, in a variety of applications it isdesirable that the glass be chemically durable or resistant toaggressive chemical agents. In particular, when using the glass as asubstrate material for microelectronic devices such as micro-LEDs, theglass should be durable to water and acids, including hydrofluoric acid(HF) and its vapor.

When used as a substrate or carrier, glass should also possess a highelastic modulus (Young's modulus) so that the glass exhibits minimumdeformation under high loads. The higher is the Young's modulus and thehigher is the thickness of the glass, the lower is the deformation of aglass substrate having particular dimensions under a given load.Alternatively, if glass with a higher Young's modulus can me madethinner while maintaining deformation under a particular load to withina specified limit.

All else being equal, however, the higher is the Young's modulus of theglass, the greater are the thermal stresses formed in the glass uponcooling. Thermal stresses may cause undesirable deformation of thearticles, e.g. warp. To reduce deformation caused by thermal stresses,it is preferable for the glass to have a low coefficient of thermalexpansion (CTE). In other words, the greater the Young's modulus and thelower the CTE of the glass, the better the glass is as a substrate orcarrier and the better is the quality of electronic devices processed onthe glass.

In some applications, it may also be desirable for glass substrate orcarrier to have a low optical dispersion. In particular, when used foroptical lenses, the lower is the dispersion of the glass, the moreprecise is the focusing of light of different wavelengths by the glassand the higher is the image quality. Also, in laser optics, the lower isthe optical dispersion, the lower is the loss of optical signal.

It can be challenging to find glasses having the desired combination ofthese properties and and especially challenging to find such glassesthat can be formed from compositions having good glass-forming ability.For example, generally speaking, high durability to HF is unlikelyavailable for glasses containing silica (SiO₂). Silica-free glasses,however, are typically not as easily formable and or as thermally stableas conventional silicate glasses. Among silica-free compositions, thecheapest and the most convenient for melting and forming are borate andphosphate glasses, which contain significant amounts of boron oxide(B₂O₃) and/or phosphorus oxide (P₂O₅). However, both of these oxides mayvolatilize when melting, thus making the resulting composition sensitiveto the changes in the melting conditions, such as melting temperatureand time, furnace atmosphere, starting materials, etc. Also, phosphateglasses typically have relatively low elastic moduli and may not bechemically durable to water and acids. In turn, both borate andphosphate glasses with high elastic moduli, besides the above-mentionedvolatilization of boron oxide when melting, may also tend to undergocrystallization and/or liquid-liquid phase separation when cooling fromthe melt.

Traditional components of glasses known to provide high elastic moduli,such as zirconia (ZrO₂), titania (TiO₂), rare earth metal oxides, niobia(Nb₂O₅) etc., may have a limited solubility in borate and/or phosphateglasses and/or cause crystallization or liquid-liquid phase separationof the glass forming melts. Also, the traditional high-moduluscomponents may increase the optical dispersion.

In view of these considerations, there is a need for silica-free glassescontaining P₂O₅ and/or B₂O₃ as major glass formers, which exhibit highelastic moduli, low CTE, high thermal and compositional stability, andhigh chemical durability. Also, in some applications it may be desirablethat the glasses have low optical dispersion.

SUMMARY

According to an embodiment of the present disclosure, a glass comprisesa plurality of components, the glass having a composition of thecomponents comprising greater than or equal to 0.3 mol. % and less thanor equal to 50.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % andless than or equal to 75.0 mol. % P₂O₅, greater than or equal to 0.5mol. % and less than or equal to 15.0 mol. % MgO, greater than or equalto 0.0 mol. % and less than or equal to 30.0 mol. % Al₂O₃, greater thanor equal to 0.0 mol. % and less than or equal to 1.0 mol. % Cu₂O+CuO,greater than or equal to 0.3 mol. % and less than or equal to 15.0 mol.% R₂O, greater than or equal to 0.0 at. % and less than or equal to 0.5at. % F, greater than or equal to 15.0 mol. % and less than or equal to75.0 mol. % P₂O₅+B₂O₃, greater than or equal to 0.8 mol. % and less thanor equal to 15.0 mol. % R₂O+RO+SnO₂+MnO₂ and greater than or equal to0.0 mol. % and less than or equal to 5.0 mol. % TeO₂+GeO₂, wherein thecomposition of the components is substantially free of SiO₂ andsubstantially free of PbO and wherein the composition of the componentssatisfies the conditions: (Li₂O+Na₂O)/R₂O [mol. %]≥0.75, where chemicalformulas mean the content of corresponding components in the glass, R₂Ois a total sum of monovalent metal oxides, and RO is a total sum ofdivalent metal oxides.

According to another embodiment of the present disclosure, a glasscomprises a plurality of components, the glass having a composition ofthe components comprising greater than or equal to 40.0 mol. % and lessthan or equal to 75.0 mol. % P₂O₅, greater than or equal to 0.5 mol. %and less than or equal to 10.5 mol. % B₂O₃, greater than or equal to 0.0mol. % and less than or equal to 25.0 mol. % Al₂O₃, greater than orequal to 0.0 mol. % and less than or equal to 0.5 mol. % SiO₂, greaterthan or equal to 0.0 at. % and less than or equal to 5.0 at. % F,greater than or equal to 0.5 mol. % R₂O+RO, greater than or equal to 0.0mol. % and less than or equal to 9.5 mol. % K₂O+Rb₂O+Cs₂O and greaterthan or equal to 0.0 mol. % and less than or equal to 0.5 mol. %ZnO+CuO+Cu₂O, wherein the composition of the components satisfies theconditions: 3*Al₂O₃+R₂O+RO−P₂O₅[mol. %]≥−7.0 and Al₂O₃−R₂O−RO [mol.%]≥7.95.

According to one more embodiment of the present disclosure, a glasscomprises a plurality of components, the glass having a composition ofthe components comprising greater than or equal to 40.0 mol. % and lessthan or equal to 75.0 mol. % P₂O₅, greater than or equal to 3.0 mol. %and less than or equal to 30.0 mol. % Al₂O₃, greater than or equal to0.0 mol. % and less than or equal to 20.0 mol. % Li₂O, greater than orequal to 0.0 mol. % and less than or equal to 15.0 mol. % ZnO, greaterthan or equal to 0.0 mol. % and less than or equal to 15.0 mol. % B₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %SiO₂, greater than or equal to 0.0 mol. % and less than or equal to 20.0mol. % RO, greater than or equal to 0.0 at. % and less than or equal to1.0 at. % F, greater than or equal to 0.5 mol. % and less than or equalto 20.0 mol. % TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂, greater than or equal to0.5 mol. % R₂O+RO+B₂O₃, greater than or equal to 0.0 mol. % and lessthan or equal to 28.0 mol. % R₂O+RO and may optionally contain one ormore components selected from MnO₂, Nb₂O₅, SnO₂, Ta₂O₅, WO₃, Sc₂O₃,Pr₂O₃, PrO₂, Pr₆O₁₁, Nd₂O₃, Eu₂O₃, EuO, Gd₂O₃, GdO₂, Tb₂O₃, Dy₂O₃,Ho₂O₃, Er₂O₃, Tm₂O₃, Yb₂O₃, Lu₂O₃ and Sm₂O₃, wherein the composition ofthe components is substantially free of Cu, Co, Cr and Ni, and the glasssatisfies the condition: P_(E)>75, where P_(E) is predicted value ofYoung's modulus, E [GPa], calculated from the glass composition in termsof mol. % of the components according to the Formula (II):

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II)

where chemical formulas mean the content of corresponding components inthe glass, RO is a total sum of divalent metal oxides, R₂O is a totalsum of monovalent metal oxides, and an asterisk (*) meansmultiplication.

These and other aspects, objects, and features of the present disclosurewill be understood and appreciated by those skilled in the art uponstudying the following specification, claims, and appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot illustrating the relationship between the Young'smodulus E and the parameter P_(E) calculated by formula (II) for someComparative Glasses and some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 2 is a plot of an exemplary cooling schedule according to a “15 mindevit test” condition for some Exemplary Glasses according to anembodiment of the present disclosure.

FIG. 3 is a plot that presents the relationship between the Young'smodulus E and the ratio P₂O₅/(3*Al₂O₃+B₂O₃) for some Exemplary Glasses.

DETAILED DESCRIPTION

In the following detailed description, for purposes of explanation andnot limitation, example embodiments disclosing specific details are setforth to provide a thorough understanding of various principles of thepresent disclosure. However, it will be apparent to one having ordinaryskill in the art, having had the benefit of the present disclosure, thatthe present disclosure may be practiced in other embodiments that departfrom the specific details disclosed herein. Moreover, descriptions ofwell-known devices, methods and materials may be omitted so as not toobscure the description of various principles of the present disclosure.Finally, wherever applicable, like reference numerals refer to likeelements.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps, or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is in no way intendedthat an order be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including, without limitation,matters of logic with respect to arrangement of steps or operationalflow; plain meaning derived from grammatical organization orpunctuation; the number or type of embodiments described in thespecification.

As used herein, the term “and/or,” when used in a list of two or moreitems, means that any one of the listed items can be employed by itself,or any combination of two or more of the listed items can be employed.For example, if a composition is described as containing components A,B, and/or C, the composition can contain A alone; B alone; C alone; Aand B in combination; A and C in combination; B and C in combination; orA, B, and C in combination.

Modifications of the disclosure will occur to those skilled in the artand to those who make or use the disclosure. Therefore, it is understoodthat the embodiments shown in the drawings and described above aremerely for illustrative purposes and not intended to limit the scope ofthe disclosure, which is defined by the following claims, as interpretedaccording to the principles of patent law, including the doctrine ofequivalents.

As used herein, the term “about” means that amounts, sizes,formulations, parameters, and other quantities and characteristics arenot and need not be exact, but may be approximate and/or larger orsmaller, as desired, reflecting tolerances, conversion factors, roundingoff, measurement error and the like, and other factors known to thoseskilled in the art. When the term “about” is used in describing a valueor an end-point of a range, the disclosure should be understood toinclude the specific value or end-point referred to. Whether or not anumerical value or end-point of a range in the specification recites“about,” the numerical value or end-point of a range is intended toinclude two embodiments: one modified by “about,” and one not modifiedby “about.” It will be further understood that the end-points of each ofthe ranges are significant both in relation to the other end-point, andindependently of the other end-point.

The term “component” refers to a material or compound included in abatch composition from which a glass is formed. Components includeoxides, including but not limited to those expressed in Formulas (I),and (II), and the claims. Representative components include B₂O₃, P₂O₅,Al₂O₃, CuO, Cu₂O, RO, R₂O, SnO₂, MnO₂, RE_(m)O_(n), SiO₂, Ta₂O₅, ZnO,WO₃, Nb₂O₅, TiO₂, ZrO₂, Bi₂O₃, TeO₂, etc. Other representativecomponents include halogens (e.g. F, Br, CI). Whenever a component isincluded as a term in a mathematical expression or formula, it isunderstood that the component refers to the amount of the component inunits of mol. % in the batch composition of the glass. For example, theexpression “B₂O₃+P₂O₅” refers to the sum of the amount of B₂O₃ in unitsof mol. % and the amount of P₂O₅ in units of mol. % in the batchcomposition of the glass. A mathematical expression or formula is anyexpression or formula that includes a mathematical operator such as “+”,“−”, “*”, “/”, “min”, or “max”.

The term “formed from” can mean one or more of comprises, consistsessentially of, or consists of. For example, a component that is formedfrom a particular material can comprise the particular material, consistessentially of the particular material, or consist of the particularmaterial.

The terms “free” and “substantially free” are used interchangeablyherein to refer to an amount and/or an absence of a particular componentin a glass composition that is not intentionally added to the glasscomposition. It is understood that the glass composition may containtraces of a particular constituent component as a contaminant or a trampin an amount of less than 0.10 mol. %.

As used herein, the term “tramp”, when used to describe a particularconstituent component in a glass composition, refers to a constituentcomponent that is not intentionally added to the glass composition andis present in an amount of less than 0.10 mol. %. Tramp components maybe unintentionally added to the glass composition as an impurity inanother constituent component and/or through migration of the trampcomponent into the composition during processing of the glasscomposition.

Unless otherwise specified, the term “glass” is used to refer to a glassmade from a glass composition disclosed herein.

The symbol “*” means multiplication when used in any formula herein.

The term “log” means logarithm in base 10.

Temperature is expressed herein in units of ° C. (degrees Celsius).

Viscosity is expressed herein in units of P (Poise).

The term “glass former” is used herein to refer to a component that,being solely present in the glass composition (i.e., without othercomponents, except for tramps), is able to form a glass when cooling themelt at a rate of not greater than about 300° C./min.

The term “modifier”, as used herein, refers to the oxides of monovalentor divalent metals, i.e., R₂O or RO, where “R” stands for a cation.Modifiers can be added to a glass composition to change the atomicstructure of the melt and the resulting glass. In some embodiments, themodifier may change the coordination numbers of cations present in theglass formers (e.g., boron in B₂O₃), which may result in forming a morepolymerized atomic network and, as a result, may provide better glassformation.

As used herein, the term “RO” refers to a total content of divalentmetal oxides (in mol. %), the term “R₂O” refers to a total content ofmonovalent metal oxides (in mol. %), and the term “Alk₂O” refers to atotal content of alkali metal oxides (in mol. %). The term R₂Oencompasses alkali metal oxides (Alk₂O), in addition to other monovalentmetal oxides, such as Ag₂O, Tl₂O, and Hg₂O, for example. As discussedbelow, in the present disclosure, a rare earth metal oxide is referredto herein by its normalized formula (RE₂O₃) in which the rare earthmetal RE has the redox state “+3,” and thus rare earth metal oxides arenot encompassed by the term RO.

As used herein, the term “rare earth metals” refers to the metals listedin the Lanthanide Series of the IUPAC Periodic Table, plus yttrium andscandium. As used herein, the term “rare earth metal oxides,” is used torefer to the oxides of rare earth metals in different redox states, suchas “+3” for lanthanum in La₂O₃, “+4” for cerium in CeO₂, “+2” foreuropium in EuO, etc. In general, the redox states of rare earth metalsin oxide glasses may vary and, in particular, the redox state may changeduring melting, based on the batch composition and/or the redoxconditions in the furnace where the glass is melted and/or heat-treated(e.g., annealed). Unless otherwise specified, a rare earth metal oxideis referred to herein by its normalized formula in which the rare earthmetal has the redox state “+3.” Accordingly, in the case in which a rareearth metal having a redox state other than “+3” is added to the glasscomposition batch, the glass compositions are recalculated by adding orremoving some oxygen to maintain the stoichiometry. For example, whenCeO₂ (with cerium in redox state “+4”) is used as a batch component, theresulting as-batched composition is recalculated assuming that two molesof CeO₂ is equivalent to one mole of Ce₂O₃, and the resulting as-batchedcomposition is expressed in terms of Ce₂O₃. As used herein, the term“RE_(m)O_(n)” is used to refer to the total content of rare earth metaloxides in all redox states present, and the term “RE₂O₃” is used torefer to the total content (in mol. %) of rare earth metal oxides in the“+3” redox state, also specified as “trivalent equivalent”.

Unless otherwise specified, all compositions are expressed in terms ofas-batched mole percent (mol %). As will be understood by those havingordinary skill in the art, various melt constituents (e.g., fluorine,alkali metals, boron, etc.) may be subject to different levels ofvolatilization (e.g., as a function of vapor pressure, melt time and/ormelt temperature) during melting of the constituents. As such, the term“about,” in relation to such constituents, is intended to encompassvalues within about 0.2 mol % when measuring final articles as comparedto the as-batched compositions provided herein. With the forgoing inmind, substantial compositional equivalence between final articles andas-batched compositions is expected. In some embodiments, whereindicated, the compositions may be expressed in terms of as-batchedpercent by weight of oxides (wt %).

In the case when fluorine or other halogen (chlorine, bromine, and/oriodine) is added to or is present in an oxide glass, the molecularrepresentation of the resulting glass composition may be expressed indifferent ways. In the present disclosure, the content of fluorine as asingle term, when present, is expressed in terms of atomic percent (at.%), which is determined based on the fraction of fluorine in a total sumof all atoms in a glass composition multiplied by a factor of 100.

In the present disclosure, the following method of representation offluorine-containing compositions and concentration ranges is used. Theconcentration limits for all oxides (e.g. SiO₂, B₂O₃, Na₂O, etc.) arepresented under the assumption that the respective cations (such as, forexample, silicon [Si₄ ⁺], boron [B₃ ⁺], sodium [Na⁺], etc.) areinitially presented in the form of the corresponding oxides. Whenfluorine is present, for the purposes of calculating the concentrationof components of the composition, some part of the oxygen in the oxideis equivalently replaced with fluorine (i.e. one atom of oxygen isreplaced with two atoms of fluorine). The said fluorine is assumed to bepresent in the form of fluorides, such as silicon fluoride (SiF₄),sodium fluoride (NaF) or others; accordingly, the total sum of alloxides and fluorides is assumed to be 100 mole percent or 100 weightpercent in all compositions.

The measured density values for the glasses reported herein weremeasured at room temperature in units of g/cm³ by Archimedes method inwater with an error of 0.001 g/cm³. As used herein, density measurementsat room temperature (specified as d_(RT)) are indicated as beingmeasured at 20° C. or 25° C., and encompass measurements obtained attemperatures that may range from 20° C. to 25° C. It is understood thatroom temperature may vary between about 20° C. to about 25° C., however,for the purposes of the present disclosure, the variation in densitywithin the temperature range of 20° C. to 25° C. is expected to be lessthan the error of 0.001 g/cm³, and thus is not expected to impact theroom temperature density measurements reported herein.

As used herein, the term “refraction” refers to the relationship of therefractive index to the density according to the ratio:(n_(d)−1)/d_(RT), where the refractive index n_(d) is measured at 587.56nm and the density d_(RT) is measured in g/cm³ at 25° C. The ratio(n_(d)−1)/d_(RT), or refraction, may characterize the relationshipbetween the refractive index n_(d) and the density d_(RT). The higherthe refraction value, the higher the refractive index is at a givendensity.

The refractive index values reported herein were measured at roomtemperature (about 25° C.), unless otherwise specified. The refractiveindex values for a glass sample were measured using a Metricon Model2010 prism coupler refractometer with an error of about ±0.0002. Usingthe Metricon, the refractive index of a glass sample was measured at twoor more wavelengths of about 406 nm, 473 nm, 532 nm, 633 nm, 828 nm, and1064 nm. The measured dependence characterizes the dispersion and wasthen fitted with a Cauchy's law equation or Sellmeier equation to allowfor calculation of the refractive index of the sample at a givenwavelength of interest between the measured wavelengths. The term“refractive index n_(d)” is used herein to refer to a refractive indexcalculated as described above at a wavelength of 587.56 nm, whichcorresponds to the helium d-line wavelength. The term “refractive indexn_(C)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 656.3 nm. The term “refractive indexn_(F)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 486.1 nm. The term “refractive indexn_(g)” is used herein to refer to a refractive index calculated asdescribed above at a wavelength of 435.8 nm.

The terms “dispersion” and “optical dispersion” are used interchangeablyto refer to a difference or ratio of the refractive indices of a glasssample at predetermined wavelengths. One numerical measure of opticaldispersion reported herein is the Abbe number, which can be calculatedby the formula: v₂=(n_(x)−1)/(n_(F)−n_(C)), where “x” in the presentdisclosure stands for one of the commonly used wavelengths (for example,587.56 nm [d-line] for v_(d) or 589.3 nm [D-line] for v_(D)), n_(x) isthe refractive index at this wavelength (for example, n_(d) for v_(d)and n_(D) for v_(D)), and n_(F) and n_(C) are refractive indices at thewavelengths 486.1 nm (F-line) and 656.3 nm (C-line), respectively. Thenumerical values of v_(d) and v_(D) differ very slightly, mostly within±0.1% to ±0.2%. As reported herein, the dispersion of a glass sample isrepresented by the Abbe number (v_(d)), which characterizes therelationship between the refractive indices of the sample at threedifferent wavelengths according to the following formula:v_(d)=(n_(d)−1)/(n_(F)−n_(C)), where n_(d) is the refractive index at587.56 nm (d-line), n_(F) is the refractive index at 486.1 nm, and n_(C)is the refractive index at 656.3 nm. A higher Abbe number corresponds toa lower optical dispersion.

The term “liquidus temperature” (T_(Uq)) is used herein to refer to atemperature above which the glass composition is completely liquid withno crystallization of constituent components of the glass.

The term “α,” or “α₂₀₋₃₀₀,” as used herein, refers to the averagecoefficient of linear thermal expansion (CTE) of the glass compositionover a temperature range from 20° C. (room temperature, or RT) to 300°C. This property is measured by using a horizontal dilatometer (push-roddilatometer) in accordance with ASTM E228-11. The numeric measure of αis a linear average value in a specified temperature range ΔT (e.g., RTto 300° C.) expressed as α=ΔL/(L₀ΔT), where L₀ is the linear size of asample at some temperature within or near the measured range, and L isthe change in the linear size (ΔL) in the measured temperature range ΔT.

The terms “modulus” and “elastic modulus” refer to Young's modulus. TheYoung's modulus (E) and the Poisson's ratio (μ) are measured by usingResonant Ultrasound Spectroscopy, using a Quasar RUSpec 4000 availablefrom ITW Indiana Private Limited, Magnaflux Division, or using Brillouinscattering method with 532 nm excitation.

The glass transition temperature (T_(g)) is measured by differentialscanning calorimeter (DSC) at the heating rate of 10 K/min after coolingin air.

The term “softening point” (T_(soft)) refers to the temperature at whichthe viscosity of the glass composition is 1076 Poise.

The terms “strain point” and “Tstrain” refer to the temperaturedetermined according to ASTM C598-93, at which the viscosity of a glassat a given glass composition is approximately 10^(14.7) Poise.

The term “liquidus viscosity” (η_(iq)) refers to the viscosity of theglass composition at the liquidus temperature of the glass composition.

The term “annealing point” (An.P.) as used herein, refers to thetemperature determined according to ASTM C598-93(2013), at which theviscosity of a glass of a given glass composition is approximately10^(13.2) Poise.

In the mathematical formulas used in the present disclosure, the term“min(A, B)” means the lesser of the values A and B, and the term “max(A,B) means the greater of the quantities A and B, where “A” and “B” may beany quantities (concentrations of components, values of properties,etc.) The term “abs(X)” means absolute value of a quantity X (withoutsign).

Glass composition may include phosphorus oxide (P₂O₅). In the glasses ofthe present disclosure, phosphorus oxide plays a role of a major glassformer, which forms the continuous atomic structure and, therefore,allows the melts to vitrify. Also, phosphorus oxide provides low opticaldispersion, which may be important when using the glasses in laseroptics. However, when the content of P₂O₅ becomes very high, someundesirable effects appear, such as low compositional stability (due tovolatilization of P₂O₅ when melting and absorption of water from thefurnace atmosphere), low chemical durability (up to being completelysoluble), etc. Accordingly, the content of phosphorus oxide ispreferably limited. In embodiments, the glass composition may containphosphorus oxide (P₂O₅) in an amount from greater than or equal to 0.0mol. % to less than or equal to 80.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain P₂O₅ in an amount greater than or equal to 0.0mol. %, greater than or equal to 10.0 mol. %, greater than or equal to30.0 mol. %, greater than or equal to 40.0 mol. %, greater than or equalto 45.0 mol. %, greater than or equal to 48.0 mol. %, greater than orequal to 50.0 mol. %, greater than or equal to 53.5 mol. %, greater thanor equal to 57.5 mol. %, greater than or equal to 58.0 mol. %, greaterthan or equal to 60.0 mol. %, or greater than or equal to 70.0 mol. %.In some other embodiments, the glass composition may contain P₂O₅ in anamount less than or equal to 80.0 mol. %, less than or equal to 75.0mol. %, less than or equal to 70.0 mol. %, less than or equal to 68.0mol. %, less than or equal to 66.0 mol. %, less than or equal to 65.1mol. %, less than or equal to 60.0 mol. %, less than or equal to 50.0mol. %, or less than or equal to 10.0 mol. %. In some more embodiments,the glass composition may contain P₂O₅ in an amount greater than orequal to 0.0 mol. % and less than or equal to 80.0 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 75.0 mol. %, greaterthan or equal to 30.0 mol. % and less than or equal to 80.0 mol. %,greater than or equal to 40.0 mol. % and less than or equal to 75.0 mol.%, greater than or equal to 45.0 mol. % and less than or equal to 75.0mol. %, greater than or equal to 48.0 mol. % and less than or equal to80.0 mol. %, greater than or equal to 50.0 mol. % and less than or equalto 70.0 mol. %, greater than or equal to 53.5 mol. % and less than orequal to 66.0 mol. %, greater than or equal to 57.48 mol. % and lessthan or equal to 65.1 mol. %, greater than or equal to 58.0 mol. % andless than or equal to 66.0 mol. %, greater than or equal to 60.0 mol. %and less than or equal to 68.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 50.0 mol. %, greater than or equal to40.0 mol. % and less than or equal to 50.0 mol. %, greater than or equalto 50.0 mol. % and less than or equal to 60.0 mol. %.

Glass composition may include boron oxide (B₂O₃). Boron oxide can beadded to the glass composition as a secondary glass former to increasethe viscosity, chemical durability and elastic moduli of the phosphateglasses, without significantly affecting their CTE. Also, boron oxideprovides low optical dispersion, which may be important when using theglasses in laser optics. However, when added in high concentrations,B₂O₃ may possibly cause liquid-liquid phase separation of the glassforming melts, which, in turn, may cause further crystallization of oneor more phases. Also, the effect of B₂O₃ on the elastic moduli isnonlinear, and at high concentrations it may not increase, but, rather,decrease the elastic moduli. Accordingly, the content of boron oxide ispreferably limited, or glass compositions may be substantially free ofB₂O₃. In embodiments, the glass composition may contain boron oxide(B₂O₃) in an amount from greater than or equal to 0.0 mol. % to lessthan or equal to 50.0 mol. % and all ranges and sub-ranges between theforegoing values. In some embodiments, the glass composition may containB₂O₃ in an amount greater than or equal to 0.0 mol. %, greater than orequal to 0.3 mol. %, greater than or equal to 0.5 mol. %, greater thanor equal to 1.5 mol. %, greater than or equal to 2.0 mol. %, greaterthan or equal to 10.0 mol. %, greater than or equal to 25.0 mol. %,greater than or equal to 35.0 mol. %, greater than or equal to 40.0 mol.%, or greater than or equal to 45.0 mol. %. In some other embodiments,the glass composition may contain B₂O₃ in an amount less than or equalto 50.0 mol. %, less than or equal to 45.0 mol. %, less than or equal to40.0 mol. %, less than or equal to 35.0 mol. %, less than or equal to30.0 mol. %, less than or equal to 25.0 mol. %, less than or equal to15.0 mol. %, less than or equal to 12.0 mol. %, less than or equal to10.0 mol. %, less than or equal to 8.0 mol. %, or less than or equal to7.75 mol. %. In some more embodiments, the glass composition may containB₂O₃ in an amount greater than or equal to 0.0 mol. % and less than orequal to 15.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 10.0 mol. %, greater than or equal to 0.5 mol. % and lessthan or equal to 10.5 mol. %, greater than or equal to 0.3 mol. % andless than or equal to 50.0 mol. %, greater than or equal to 0.3 mol. %and less than or equal to 12.0 mol. %, greater than or equal to 0.5 mol.% and less than or equal to 30.0 mol. %, greater than or equal to 0.5mol. % and less than or equal to 8.0 mol. %, greater than or equal to1.5 mol. % and less than or equal to 7.75 mol. %, greater than or equalto 2.01 mol. % and less than or equal to 7.94 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 50.0 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 7.75 mol. %, greaterthan or equal to 0.3 mol. % and less than or equal to 7.75 mol. %,greater than or equal to 0.5 mol. % and less than or equal to 7.75 mol.%, greater than or equal to 1.5 mol. % and less than or equal to 50.0mol. %, greater than or equal to 2.0 mol. % and less than or equal to50.0 mol. %, greater than or equal to 2.0 mol. % and less than or equalto 7.75 mol. %, greater than or equal to 25.0 mol. % and less than orequal to 50.0 mol. %.

Glass composition may include monovalent metal oxides (R₂O). Monovalentmetal oxides, such as alkali metal oxides (Li₂O, Na₂O, K₂O, Rb₂O andCs₂O), silver oxide (Ag₂O), copper oxide (Cu₂O) and others can be addedto the glass compositions to improve the thermal stability and chemicaldurability and reduce volatilization of P₂O₅ when melting, allowing tobatch more P₂O₅ with solid materials like, for example, monovalent metalmetaphosphates (RPO₃ where “R” refers to a metal cation). However, mostof monovalent metal oxides either provide relatively low elastic moduli(except for Li₂O), or provide high CTE (except for Cu₂O), or both.Accordingly, the content of monovalent metal oxides is preferablylimited, or glass compositions may be substantially free of R₂O.

In some embodiments, the glass composition may contain monovalent metaloxides R₂O in an amount greater than or equal to 0.3 mol. %, greaterthan or equal to 10.0 mol. %, or greater than or equal to 20.0 mol. %.In some other embodiments, the glass composition may contain monovalentmetal oxides R₂O in an amount less than or equal to 28.0 mol. %, lessthan or equal to 20.0 mol. %, less than or equal to 15.0 mol. %, or lessthan or equal to 10.0 mol. %. In some more embodiments, the glasscomposition may contain R₂O in an amount greater than or equal to 0.3mol. % and less than or equal to 15.0 mol. %, greater than or equal to0.3 mol. % and less than or equal to 28.0 mol. %, greater than or equalto 0.3 mol. % and less than or equal to 20.0 mol. %, or greater than orequal to 0.3 mol. % and less than or equal to 10.0 mol. %, greater thanor equal to 10.0 mol. % and less than or equal to 28.0 mol. %, greaterthan or equal to 10.0 mol. % and less than or equal to 20.0 mol. %, orgreater than or equal to 10.0 mol. % and less than or equal to 15.0 mol.%.

Glass composition may include lithium oxide (Li₂O). Lithium oxide can beadded to the glass compositions to increase the elastic moduli. Also,adding Li₂O may increase the solubility of other high-moduluscomponents, such as, for example, TiO₂, Nb₂O₅, rare earth metal oxidesand others, in the glass forming melts. However, at high concentrations,Li₂O may decrease the high-temperature viscosity, which may causedevitrification of the glass forming melts. Also, Li₂O provides a ratherhigh CTE, which may cause wrapping or breakage of the glass articlesbecause of high thermal stresses. Accordingly, the content of lithiumoxide is preferably limited, or glass compositions may be substantiallyfree of Li₂O. In embodiments, the glass composition may contain lithiumoxide (Li₂O) in an amount from greater than or equal to 0.0 mol. % toless than or equal to 20.0 mol. % and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass composition maycontain Li₂O in an amount greater than or equal to 0.0 mol. %, greaterthan or equal to 2.0 mol. %, greater than or equal to 5.0 mol. %,greater than or equal to 10.0 mol. %, greater than or equal to 14.0 mol.%, greater than or equal to 16.0 mol. %, or greater than or equal to18.0 mol. %. In some other embodiments, the glass composition maycontain Li₂O in an amount less than or equal to 20.0 mol. %, less thanor equal to 18.0 mol. %, less than or equal to 16.0 mol. %, less than orequal to 15.0 mol. %, less than or equal to 14.0 mol. %, less than orequal to 10.0 mol. %, less than or equal to 9.0 mol. %, less than orequal to 8.0 mol. %, less than or equal to 7.0 mol. %, or less than orequal to 5.0 mol. %. In some more embodiments, the glass composition maycontain Li₂O in an amount greater than or equal to 0.0 mol. % and lessthan or equal to 20.0 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 14.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 0.0mol. % and less than or equal to 9.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 8.0 mol. %, greater than or equalto 1.87 mol. % and less than or equal to 7.49 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 5.0 mol. %, greater thanor equal to 2.0 mol. % and less than or equal to 5.0 mol. %, greaterthan or equal to 10.0 mol. % and less than or equal to 20.0 mol. %,greater than or equal to 14.0 mol. % and less than or equal to 15.0 mol.%.

Glass composition may include sodium oxide (Na₂O). Sodium oxide can beadded to the glass compositions to improve the chemical durability toalkalis and acids. Also, addition of Na₂O may increase the solubility ofhigh-modulus components, such as, for example, TiO₂, Nb₂O₅, rare earthmetal oxides and others. In the presence of B₂O₃, the addition of Na₂Omay also indirectly increase the impact of B₂O₃ on the elastic modulidue to a transition of boron cations from trifold to fourfoldcoordination. However, Na₂O provides high CTE, which may increase thethermal stresses. Also, sodium oxide, especially when a glasscomposition does not contain B₂O₃, provides relatively low elasticmodulus. Accordingly, the content of sodium oxide is preferably limited,or glass compositions may be substantially free of Na₂O. In embodiments,the glass composition may contain sodium oxide (Na₂O) in an amount fromgreater than or equal to 0.0 mol. % to less than or equal to 10.0 mol. %and all ranges and sub-ranges between the foregoing values. In someembodiments, the glass composition may contain Na₂O in an amount greaterthan or equal to 0.0 mol. %, greater than or equal to 5.0 mol. %,greater than or equal to 7.0 mol. %, greater than or equal to 8.0 mol.%, or greater than or equal to 9.0 mol. %. In some other embodiments,the glass composition may contain Na₂O in an amount less than or equalto 10.0 mol. %, less than or equal to 9.0 mol. %, less than or equal to8.0 mol. %, less than or equal to 7.0 mol. %, less than or equal to 5.0mol. %, or less than or equal to 4.0 mol. %. In some more embodiments,the glass composition may contain Na₂O in an amount greater than orequal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 9.0 mol. %, greaterthan or equal to 0.0 mol. % and less than or equal to 8.0 mol. %,greater than or equal to 0.02 mol. % and less than or equal to 3.54 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 4.0mol. %, greater than or equal to 5.0 mol. % and less than or equal to10.0 mol. %, greater than or equal to 5.0 mol. % and less than or equalto 7.0 mol. %, greater than or equal to 7.0 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 7.0 mol. % and less thanor equal to 8.0 mol. %, greater than or equal to 8.0 mol. % and lessthan or equal to 10.0 mol. %, greater than or equal to 8.0 mol. % andless than or equal to 9.0 mol. %.

Glass composition may include potassium oxide (K₂O). Potassium oxide canbe added to the glass compositions to improve thermal stability andchemical durability. However, K₂O provides low elastic modulus and highCTE. Accordingly, the content of potassium oxide is preferably limited,or glass compositions may be substantially free of K₂O. In embodiments,the glass composition may contain potassium oxide (K₂O) in an amountfrom greater than or equal to 0.0 mol. % to less than or equal to 5.0mol. % and all ranges and sub-ranges between the foregoing values. Insome other embodiments, the glass composition may contain K₂O in anamount less than or equal to 5.0 mol. %, less than or equal to 9.0 mol.%, less than or equal to 8.0 mol. %, less than or equal to 5.0 mol. %,less than or equal to 2.5 mol. %, or less than or equal to 0.99 mol. %.In some more embodiments, the glass composition may contain K₂O in anamount greater than or equal to 0.0 mol. % and less than or equal to10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 9.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 8.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 5.0 mol. %, greater than or equal to 0.0 mol. % and lessthan or equal to 1.0 mol. %, greater than or equal to 0.02 mol. % andless than or equal to 0.99 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 0.99 mol. %.

Glass composition may include divalent metal oxides (RO). Divalent metaloxides, such as alkaline earth metal oxides (BeO, MgO, CaO, SrO andBaO), zinc oxide (ZnO), manganese oxide (MnO), cadmium oxide (CdO) andothers can be added to the glass composition for better thermalstability and chemical durability. Also, their addition can increase thesolubility of high-modulus components, such as titania (TiO₂), rareearth metal oxides (RE_(m)O_(n)) and others. However, when added in highconcentrations, divalent metal oxides can increase the liquidustemperature of the glass and/or decrease the high-temperature viscosity,which may cause crystallization of the glass forming melts when formingand cooling glass articles. Accordingly, the content of divalent metaloxides is preferably limited, or glass compositions may be substantiallyfree of RO.

In some embodiments, the glass composition may contain divalent metaloxides RO in an amount greater than or equal to 0.0 mol. %, greater thanor equal to 10.0 mol. %, or greater than or equal to 20.0 mol. %. Insome other embodiments, the glass composition may contain divalent metaloxides RO in an amount less than or equal to 25.0 mol. %, less than orequal to 20.0 mol. %, less than or equal to 15.0 mol. %, or less than orequal to 10.0 mol. %. In some more embodiments, the glass compositionmay contain RO in an amount greater than or equal to 0.0 mol. % and lessthan or equal to 25.0 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 20.0 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 15.0 mol. %, or greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, greater than or equal to10.0 mol. % and less than or equal to 25.0 mol. %, greater than or equalto 10.0 mol. % and less than or equal to 20.0 mol. %, or greater than orequal to 10.0 mol. % and less than or equal to 15.0 mol. %.

Glass composition may include magnesia (MgO). Magnesia can be added tothe glass compositions to increase the elastic modulus. However, at highconcentrations MgO can cause precipitation of the refractory minerals,such as magnesium phosphate Mg₃P₂O₈, magnesium aluminate MgAl₂O₄,magnesium titanate MgTiO₃ and others, at high temperatures, which maycause devitrification of the glass forming melts. Accordingly, thecontent of magnesia is preferably limited, or glass compositions may besubstantially free of MgO. In embodiments, the glass composition maycontain magnesia (MgO) in an amount from greater than or equal to 0.0mol. % to less than or equal to 20.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain MgO in an amount greater than or equal to 0.0mol. %, greater than or equal to 0.5 mol. %, greater than or equal to0.75 mol. %, greater than or equal to 1.5 mol. %, greater than or equalto 2.0 mol. %, greater than or equal to 5.0 mol. %, greater than orequal to 10.0 mol. %, greater than or equal to 14.0 mol. %, greater thanor equal to 16.0 mol. %, or greater than or equal to 18.0 mol. %. Insome other embodiments, the glass composition may contain MgO in anamount less than or equal to 20.0 mol. %, less than or equal to 18.0mol. %, less than or equal to 16.0 mol. %, less than or equal to 15.0mol. %, less than or equal to 14.0 mol. %, less than or equal to 10.0mol. %, less than or equal to 7.25 mol. %, less than or equal to 7.0mol. %, less than or equal to 6.25 mol. %, or less than or equal to 5.0mol. %. In some more embodiments, the glass composition may contain MgOin an amount greater than or equal to 0.0 mol. % and less than or equalto 20.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 0.5 mol. % and less thanor equal to 15.0 mol. %, greater than or equal to 0.75 mol. % and lessthan or equal to 7.25 mol. %, greater than or equal to 1.5 mol. % andless than or equal to 6.25 mol. %, greater than or equal to 2.33 mol. %and less than or equal to 6.55 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 5.0 mol. %, greater than or equal to 0.5mol. % and less than or equal to 20.0 mol. %, greater than or equal to0.5 mol. % and less than or equal to 5.0 mol. %, greater than or equalto 0.75 mol. % and less than or equal to 20.0 mol. %, greater than orequal to 2.0 mol. % and less than or equal to 5.0 mol. %.

Glass composition may include zinc oxide (ZnO). In embodiments, theglass composition may contain zinc oxide (ZnO) in an amount from greaterthan or equal to 0.0 mol. % to less than or equal to 15.0 mol. % and allranges and sub-ranges between the foregoing values. In some embodiments,the glass composition may contain ZnO in an amount greater than or equalto 0.0 mol. %, greater than or equal to 5.0 mol. %, greater than orequal to 9.0 mol. %, greater than or equal to 10.0 mol. %, greater thanor equal to 11.0 mol. %, or greater than or equal to 13.0 mol. %. Insome other embodiments, the glass composition may contain ZnO in anamount less than or equal to 15.0 mol. %, less than or equal to 13.0mol. %, less than or equal to 11.0 mol. %, less than or equal to 10.0mol. %, less than or equal to 9.0 mol. %, or less than or equal to 5.0mol. %. In some more embodiments, the glass composition may contain ZnOin an amount greater than or equal to 0.0 mol. % and less than or equalto 15.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 5.0 mol. %, greater than or equal to 5.0 mol. % and less thanor equal to 15.0 mol. %, greater than or equal to 5.0 mol. % and lessthan or equal to 9.0 mol. %, greater than or equal to 9.0 mol. % andless than or equal to 15.0 mol. %, greater than or equal to 9.0 mol. %and less than or equal to 10.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 15.0 mol. %, greater than or equal to10.0 mol. % and less than or equal to 11.0 mol. %, greater than or equalto 11.0 mol. % and less than or equal to 15.0 mol. %, greater than orequal to 11.0 mol. % and less than or equal to 13.0 mol. %.

Glass composition may include calcium oxide (CaO). Calcium oxide can beadded to the glass compositions to increase the elastic modulus andimprove chemical durability to alkalis and acids. Also, adding CaO canincrease the solubility of other high-modulus components (TiO₂, La₂O₃,Nb₂O₅ and others) in the glass forming melts. However, when added inhigh concentrations, CaO can cause crystallization of refractoryminerals (calcium phosphate Ca₃P₂O₈, calcium titanate CaTiO₃, calciumaluminate CaAl₂O₄ and others) at high temperatures, which may causedevitrification of the glass forming melts. Accordingly, the content ofcalcium oxide is preferably limited, or glass compositions may besubstantially free of CaO. In embodiments, the glass composition maycontain calcium oxide (CaO) in an amount from greater than or equal to0.0 mol. % to less than or equal to 10.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain CaO in an amount greater than or equal to 0.0mol. %, or greater than or equal to 5.0 mol. %. In some otherembodiments, the glass composition may contain CaO in an amount lessthan or equal to 10.0 mol. %, less than or equal to 5.0 mol. %, lessthan or equal to 4.0 mol. %, less than or equal to 3.4 mol. %, or lessthan or equal to 0.6 mol. %. In some more embodiments, the glasscomposition may contain CaO in an amount greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 4.0 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 3.4 mol. %, greater than orequal to 0.02 mol. % and less than or equal to 0.6 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 0.6 mol. %.

Glass composition may include lead oxide (PbO). Lead oxide can be addedto the glass compositions for better thermal stability. However, itprovides low elastic modulus and relatively high CTE. Also, PbO mayraise environmental concerns. Accordingly, the content of lead oxide ispreferably limited, or glass compositions may be substantially free ofPbO. In embodiments, the glass composition may contain lead oxide (PbO)in an amount from greater than or equal to 0.0 mol. % to less than orequal to 5.0 mol. % and all ranges and sub-ranges between the foregoingvalues. In some other embodiments, the glass composition may contain PbOin an amount less than or equal to 5.0 mol. %, less than or equal to 2.5mol. %, or less than or equal to 0.1 mol. %. In some more embodiments,the glass composition may contain PbO in an amount greater than or equalto 0.0 mol. % and less than or equal to 0.1 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 5.0 mol. %.

Glass composition may include Cu₂O+CuO (Cu₂O+CuO). Copper oxides can beadded in the glass compositions in small amounts to decrease the CTE.However, copper oxides adversely decrease the Young's modulus and alsomay provide undesirable coloring. Accordingly, the content of Cu₂O+CuOis preferably limited, or glass compositions may be substantially freeof copper oxides. In embodiments, the glass composition may containCu₂O+CuO in an amount from greater than or equal to 0.0 mol. % to lessthan or equal to 5.0 mol. % and all ranges and sub-ranges between theforegoing values. In some other embodiments, the glass composition maycontain Cu₂O+CuO in an amount less than or equal to 5.0 mol. %, lessthan or equal to 2.5 mol. %, or less than or equal to 1.0 mol. %. Insome more embodiments, the glass composition may contain Cu₂O+CuO in anamount greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. %, greater than or equal to 0.0 mol. % and less than or equal to5.0 mol. %.

Glass composition may include silica (SiO₂). In glasses of the presentdisclosure, silica can be added as a secondary glass former in the casewhen high durability to hydrofluoric acid (HF) and its vapor is notrequired. However, adding silica to phosphate glasses may causeliquid-liquid phase separation and further devitrification. Also, in thecases when durability to HF or its vapor is demanded, addition of SiO₂is undesirable because of the leaching of silicon in the form of SiF₄and surface degradation. Accordingly, the content of silica ispreferably limited, or glass compositions may be substantially free ofSiO₂. In embodiments, the glass composition may contain silica (SiO₂) inan amount from greater than or equal to 0.0 mol. % to less than or equalto 5.0 mol. % and all ranges and sub-ranges between the foregoingvalues. In some other embodiments, the glass composition may containSiO₂ in an amount less than or equal to 5.0 mol. %, less than or equalto 3.0 mol. %, less than or equal to 2.5 mol. %, less than or equal to1.0 mol. %, less than or equal to 0.2 mol. %, or less than or equal to0.1 mol. %. In some more embodiments, the glass composition may containSiO₂ in an amount greater than or equal to 0.0 mol. % and less than orequal to 3.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. %, greater than or equal to 0.0 mol. % and lessthan or equal to 0.5 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 0.2 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 0.1 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 5.0 mol. %.

Glass composition may include tungsten oxide (WO₃). In embodiments, theglass composition may contain tungsten oxide (WO₃) in an amount fromgreater than or equal to 0.0 mol. % to less than or equal to 29.0 mol. %and all ranges and sub-ranges between the foregoing values. In someembodiments, the glass composition may contain WO₃ in an amount greaterthan or equal to 0.0 mol. %, greater than or equal to 10.0 mol. %,greater than or equal to 19.5 mol. %, or greater than or equal to 20.0mol. %. In some other embodiments, the glass composition may contain WO₃in an amount less than or equal to 29.0 mol. %, less than or equal to20.6 mol. %, less than or equal to 20.0 mol. %, or less than or equal to10.0 mol. %. In some more embodiments, the glass composition may containWO₃ in an amount greater than or equal to 0.0 mol. % and less than orequal to 20.0 mol. %, greater than or equal to 19.5 mol. % and less thanor equal to 20.55 mol. %, greater than or equal to 0.0 mol. % and lessthan or equal to 29.0 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. %and less than or equal to 29.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 20.0 mol. %, greater than or equal to19.5 mol. % and less than or equal to 29.0 mol. %, greater than or equalto 19.5 mol. % and less than or equal to 20.0 mol. %.

Glass composition may include niobia (Nb₂O₅). In embodiments, the glasscomposition may contain niobia (Nb₂O₅) in an amount from greater than orequal to 0.0 mol. % to less than or equal to 24.0 mol. % and all rangesand sub-ranges between the foregoing values. In some embodiments, theglass composition may contain Nb₂O₅ in an amount greater than or equalto 0.0 mol. %, greater than or equal to 10.0 mol. %, greater than orequal to 15.7 mol. %, or greater than or equal to 20.0 mol. %. In someother embodiments, the glass composition may contain Nb₂O₅ in an amountless than or equal to 24.0 mol. %, less than or equal to 20.0 mol. %,less than or equal to 16.8 mol. %, or less than or equal to 10.0 mol. %.In some more embodiments, the glass composition may contain Nb₂O₅ in anamount greater than or equal to 0.0 mol. % and less than or equal to20.0 mol. %, greater than or equal to 15.7 mol. % and less than or equalto 16.75 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 24.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and lessthan or equal to 24.0 mol. %, greater than or equal to 10.0 mol. % andless than or equal to 16.8 mol. %, greater than or equal to 15.7 mol. %and less than or equal to 24.0 mol. %, greater than or equal to 15.7mol. % and less than or equal to 16.8 mol. %.

Glass composition may include yttria (Y₂O₃). In the glasses of thepresent disclosure, yttria and other rare earth metal oxides (La₂O₃,CeO₂ and others), increase elastic modulus. However, when added at highconcentrations, yttria may cause crystallization of the glass formingmelts because of precipitation of the refractory minerals, such as, forexample, yttrium phosphate (YPO₄), yttrium aluminate (Y₃Al₅O₁₂) andothers. Also, yttria is more expensive than La₂O₃ and CeO₂. Accordingly,the content of yttria is preferably limited, or glass compositions maybe substantially free of Y₂O₃. In embodiments, the glass composition maycontain yttria (Y₂O₃) in an amount from greater than or equal to 0.0mol. % to less than or equal to 20.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain Y₂O₃ in an amount greater than or equal to 0.0mol. %, greater than or equal to 1.0 mol. %, greater than or equal to5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equalto 14.0 mol. %, greater than or equal to 16.0 mol. %, or greater than orequal to 18.0 mol. %. In some other embodiments, the glass compositionmay contain Y₂O₃ in an amount less than or equal to 20.0 mol. %, lessthan or equal to 18.0 mol. %, less than or equal to 16.0 mol. %, lessthan or equal to 14.0 mol. %, less than or equal to 10.0 mol. %, lessthan or equal to 7.5 mol. %, less than or equal to 6.0 mol. %, less thanor equal to 5.5 mol. %, less than or equal to 5.0 mol. %, or less thanor equal to 4.75 mol. %. In some more embodiments, the glass compositionmay contain Y₂O₃ in an amount greater than or equal to 0.0 mol. % andless than or equal to 7.5 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 6.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 5.5 mol. %, greater than or equal to 0.0mol. % and less than or equal to 4.75 mol. %, greater than or equal to0.9 mol. % and less than or equal to 4.79 mol. %, greater than or equalto 0.0 mol. % and less than or equal to 20.0 mol. %, greater than orequal to 1.0 mol. % and less than or equal to 20.0 mol. %, greater thanor equal to 1.0 mol. % and less than or equal to 4.75 mol. %, greaterthan or equal to 10.0 mol. % and less than or equal to 14.0 mol. %,greater than or equal to 14.0 mol. % and less than or equal to 16.0 mol.%.

Glass composition may include zirconia (ZrO₂). Zirconia, like titania,can be added to the glass compositions to increase the elastic modulus,at the same time increasing the high-temperature viscosity anddecreasing CTE. However, when being added at high concentrations,especially in the absence of La₂O₃ and B₂O₃, zirconia may precipitatefrom the glass forming melts, causing their devitrification.Accordingly, the content of zirconia is preferably limited, or glasscompositions may be substantially free of ZrO₂. In embodiments, theglass composition may contain zirconia (ZrO₂) in an amount from greaterthan or equal to 0.0 mol. % to less than or equal to 20.0 mol. % and allranges and sub-ranges between the foregoing values. In some embodiments,the glass composition may contain ZrO₂ in an amount greater than orequal to 0.0 mol. %, greater than or equal to 1.0 mol. %, greater thanor equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greaterthan or equal to 14.0 mol. %, greater than or equal to 16.0 mol. %, orgreater than or equal to 18.0 mol. %. In some other embodiments, theglass composition may contain ZrO₂ in an amount less than or equal to20.0 mol. %, less than or equal to 18.0 mol. %, less than or equal to16.0 mol. %, less than or equal to 14.0 mol. %, less than or equal to10.0 mol. %, less than or equal to 7.5 mol. %, less than or equal to 7.0mol. %, less than or equal to 5.0 mol. %, less than or equal to 4.0 mol.%, less than or equal to 3.6 mol. %, or less than or equal to 3.2 mol.%. In some more embodiments, the glass composition may contain ZrO₂ inan amount greater than or equal to 0.0 mol. % and less than or equal to7.5 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 4.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 3.6 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 3.2 mol. %, greater than or equal to 0.67 mol. % and lessthan or equal to 7.01 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 20.0 mol. %, greater than or equal to 1.0 mol. %and less than or equal to 3.2 mol. %, greater than or equal to 5.0 mol.% and less than or equal to 7.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 14.0 mol. %, greater than or equal to14.0 mol. % and less than or equal to 20.0 mol. %, greater than or equalto 14.0 mol. % and less than or equal to 16.0 mol. %.

Glass composition may include cerium oxide (CeO₂). Cerium oxides (CeO₂and Ce₂O₃) can be added to the glass compositions to increase theelastic modulus. Also, adding CeO₂ can help to reduce undesirablecoloring when adding other species, such as, for example, TiO₂, due tooxidation of their cations (e.g. Ti³⁺ to Ti⁴⁺). However, when added inhigh concentrations, cerium oxides may cause precipitation of refractoryminerals (cerium phosphate CePO₄, cerium aluminate Ce₃Al₅O₁₂ and others)at high temperatures, which may cause devitrification of the glassarticles. Also, at high concentrations CeO₂ may provide undesirablecoloring. Accordingly, the content of cerium oxide is preferablylimited, or glass compositions may be substantially free of CeO₂. Inembodiments, the glass composition may contain cerium oxide (CeO₂) in anamount from greater than or equal to 0.0 mol. % to less than or equal to20.0 mol. % and all ranges and sub-ranges between the foregoing values.In some embodiments, the glass composition may contain CeO₂ in an amountgreater than or equal to 0.0 mol. %, greater than or equal to 5.0 mol.%, greater than or equal to 10.0 mol. %, greater than or equal to 14.0mol. %, greater than or equal to 16.0 mol. %, or greater than or equalto 18.0 mol. %. In some other embodiments, the glass composition maycontain CeO₂ in an amount less than or equal to 20.0 mol. %, less thanor equal to 18.0 mol. %, less than or equal to 16.0 mol. %, less than orequal to 14.0 mol. %, less than or equal to 10.0 mol. %, less than orequal to 7.5 mol. %, less than or equal to 6.5 mol. %, less than orequal to 5.75 mol. %, or less than or equal to 5.0 mol. %. In some moreembodiments, the glass composition may contain CeO₂ in an amount greaterthan or equal to 0.0 mol. % and less than or equal to 10.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 6.5mol. %, greater than or equal to 0.0 mol. % and less than or equal to5.75 mol. %, greater than or equal to 0.48 mol. % and less than or equalto 5.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 20.0 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 5.0 mol. %, greater than or equal to 5.0 mol. % and lessthan or equal to 5.75 mol. %, greater than or equal to 10.0 mol. % andless than or equal to 20.0 mol. %, greater than or equal to 10.0 mol. %and less than or equal to 14.0 mol. %, greater than or equal to 16.0mol. % and less than or equal to 20.0 mol. %, greater than or equal to16.0 mol. % and less than or equal to 18.0 mol. %.

Glass composition may include titania (TiO₂). Titania can be added tothe glass compositions to increase the elastic modulus, at the same timedecreasing the CTE and increasing the high-temperature viscosity.However, when added at high concentrations, TiO₂ may provide undesirabledark coloring. Also, TiO₂ may sometimes cause liquid-liquid phaseseparation and/or crystallization of the glass forming melts at hightemperatures due to precipitation of refractory minerals, such as, forexample, titanium phosphate TiP₂O₇, aluminum titanate Al₂TiO₅ andothers. Also, TiO₂ provides high optical dispersion. Accordingly, thecontent of titania is preferably limited, or glass compositions may besubstantially free of TiO₂. In embodiments, the glass composition maycontain titania (TiO₂) in an amount from greater than or equal to 0.0mol. % to less than or equal to 20.0 mol. % and all ranges andsub-ranges between the foregoing values. In some embodiments, the glasscomposition may contain TiO₂ in an amount greater than or equal to 0.0mol. %, greater than or equal to 1.4 mol. %, greater than or equal to5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equalto 14.0 mol. %, greater than or equal to 16.0 mol. %, or greater than orequal to 18.0 mol. %. In some other embodiments, the glass compositionmay contain TiO₂ in an amount less than or equal to 20.0 mol. %, lessthan or equal to 18.0 mol. %, less than or equal to 16.0 mol. %, lessthan or equal to 15.0 mol. %, less than or equal to 14.0 mol. %, lessthan or equal to 11.0 mol. %, less than or equal to 10.2 mol. %, lessthan or equal to 10.0 mol. %, or less than or equal to 5.0 mol. %. Insome more embodiments, the glass composition may contain TiO₂ in anamount greater than or equal to 0.0 mol. % and less than or equal to15.0 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 11.0 mol. %, greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 1.41 mol. % and less thanor equal to 10.21 mol. %, greater than or equal to 0.0 mol. % and lessthan or equal to 20.0 mol. %, greater than or equal to 1.4 mol. % andless than or equal to 5.0 mol. %, greater than or equal to 5.0 mol. %and less than or equal to 20.0 mol. %, greater than or equal to 5.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 10.0mol. % and less than or equal to 10.2 mol. %, greater than or equal to14.0 mol. % and less than or equal to 15.0 mol. %.

Glass composition may include lanthanum oxide (La₂O₃). Lanthanum oxideworks similar to cerium oxide (CeO₂) and other rare earth metal oxides(Y₂O₃, Gd₂O₃, Nd₂O₃, Tb₂O₃ and others), increasing the elastic modulus.Also, lanthanum oxide can increase the solubility of other high-moduluscomponents, such as, for example, ZrO₂, in the glass forming melts, thusimproving the thermal stability at high elastic modulus. However, whenadded in high concentrations, La₂O₃ may unacceptably increase the CTE,which may cause warping of thin articles because of thermal stresses.Also, at high concentrations, La₂O₃ may cause precipitation ofrefractory minerals (for example, lanthanum phosphate LaPO₄) at hightemperatures, which may cause devitrification of the melts. Accordingly,the content of lanthanum oxide is preferably limited, or glasscompositions may be substantially free of La₂O₃. In embodiments, theglass composition may contain lanthanum oxide (La₂O₃) in an amount fromgreater than or equal to 0.0 mol. % to less than or equal to 32.0 mol. %and all ranges and sub-ranges between the foregoing values. In someembodiments, the glass composition may contain La₂O₃ in an amountgreater than or equal to 0.0 mol. %, greater than or equal to 2.0 mol.%, greater than or equal to 5.0 mol. %, greater than or equal to 10.0mol. %, greater than or equal to 20.0 mol. %, greater than or equal to26.0 mol. %, greater than or equal to 28.0 mol. %, or greater than orequal to 30.0 mol. %. In some other embodiments, the glass compositionmay contain La₂O₃ in an amount less than or equal to 32.0 mol. %, lessthan or equal to 30.0 mol. %, less than or equal to 28.0 mol. %, lessthan or equal to 26.0 mol. %, less than or equal to 20.0 mol. %, lessthan or equal to 17.0 mol. %, less than or equal to 10.0 mol. %, lessthan or equal to 7.5 mol. %, less than or equal to 5.5 mol. %, less thanor equal to 5.0 mol. %, or less than or equal to 4.75 mol. %. In somemore embodiments, the glass composition may contain La₂O₃ in an amountgreater than or equal to 0.0 mol. % and less than or equal to 20.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 7.5mol. %, greater than or equal to 0.0 mol. % and less than or equal to5.5 mol. %, greater than or equal to 0.0 mol. % and less than or equalto 4.75 mol. %, greater than or equal to 2.19 mol. % and less than orequal to 16.89 mol. %, greater than or equal to 0.0 mol. % and less thanor equal to 32.0 mol. %, greater than or equal to 2.0 mol. % and lessthan or equal to 4.75 mol. %, greater than or equal to 5.0 mol. % andless than or equal to 32.0 mol. %, greater than or equal to 20.0 mol. %and less than or equal to 26.0 mol. %.

Glass composition may include alumina (Al₂O₃). Alumina provides highviscosity, which increases liquidus viscosity and, therefore, preventscrystallization when forming and cooling the glass articles. Also,alumina may increase chemical durability of glasses. However, whenadding Al₂O₃ in the glass composition in high concentration, it maycause precipitation of refractory minerals (aluminum phosphate AlPO₄,yttrium aluminate Y₃Al₅O₁₂, aluminum titanate Al₂TiO₅ and others) athigh temperatures, which could increase the liquidus temperature and maycause crystallization of melt when cooling and forming glass articles.Accordingly, the content of alumina is preferably limited. Inembodiments, the glass composition may contain alumina (Al₂O₃) in anamount from greater than or equal to 0.0 mol. % to less than or equal to30.0 mol. % and all ranges and sub-ranges between the foregoing values.In some embodiments, the glass composition may contain Al₂O₃ in anamount greater than or equal to 0.0 mol. %, greater than or equal to 3.0mol. %, greater than or equal to 5.0 mol. %, greater than or equal to8.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equalto 15.0 mol. %, greater than or equal to 15.5 mol. %, greater than orequal to 16.0 mol. %, greater than or equal to 20.0 mol. %, greater thanor equal to 24.0 mol. %, greater than or equal to 26.0 mol. %, orgreater than or equal to 28.0 mol. %. In some other embodiments, theglass composition may contain Al₂O₃ in an amount less than or equal to30.0 mol. %, less than or equal to 28.5 mol. %, less than or equal to28.0 mol. %, less than or equal to 27.0 mol. %, less than or equal to26.0 mol. %, less than or equal to 24.0 mol. %, less than or equal to20.0 mol. %, less than or equal to 17.5 mol. %, less than or equal to10.0 mol. %, or less than or equal to 5.0 mol. %. In some moreembodiments, the glass composition may contain Al₂O₃ in an amountgreater than or equal to 0.0 mol. % and less than or equal to 30.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 25.0mol. %, greater than or equal to 3.0 mol. % and less than or equal to30.0 mol. %, greater than or equal to 8.0 mol. % and less than or equalto 30.0 mol. %, greater than or equal to 10.0 mol. % and less than orequal to 30.0 mol. %, greater than or equal to 15.0 mol. % and less thanor equal to 20.0 mol. %, greater than or equal to 15.5 mol. % and lessthan or equal to 28.5 mol. %, greater than or equal to 15.5 mol. % andless than or equal to 17.5 mol. %, greater than or equal to 16.0 mol. %and less than or equal to 27.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 5.0 mol. %, greater than or equal to 3.0mol. % and less than or equal to 5.0 mol. %, greater than or equal to5.0 mol. % and less than or equal to 10.0 mol. %, greater than or equalto 10.0 mol. % and less than or equal to 17.5 mol. %, greater than orequal to 15.0 mol. % and less than or equal to 17.5 mol. %.

Glass composition may include fluorine (F). Fluorine can be added to theglass composition in a small concentration as a fining agent. However,fluorine raises environmental concerns. Accordingly, the content offluorine is preferably limited, or glass compositions may besubstantially free of F. In embodiments, the glass composition maycontain fluorine (F) in an amount from greater than or equal to 0.0 at.% to less than or equal to 5.0 at. % and all ranges and sub-rangesbetween the foregoing values. In some other embodiments, the glasscomposition may contain F in an amount less than or equal to 1.0 at. %,less than or equal to 0.5 at. %, or less than or equal to 0.1 at. %. Insome more embodiments, the glass composition may contain F in an amountgreater than or equal to 0.0 at. % and less than or equal to 1.0 at. %,greater than or equal to 0.0 at. % and less than or equal to 0.5 at. %,greater than or equal to 0.0 at. % and less than or equal to 0.1 at. %.

In some embodiments, the glass composition may have a sum ofAlk₂O+MgO+RE_(m)O_(n) greater than or equal to 0.0 mol. %, greater thanor equal to 0.3 mol. %, or greater than or equal to 20.0 mol. %. In someother embodiments, the glass composition may have a sum ofAlk₂O+MgO+RE_(m)O_(n) less than or equal to 40.0 mol. % or less than orequal to 20.0 mol. %. In some more embodiments, the glass compositionmay have a sum of Alk₂O+MgO+RE_(m)O_(n) greater than or equal to 0.3mol. % and less than or equal to 40.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 40.0 mol. %, or greater than orequal to 0.0 mol. % and less than or equal to 20.0 mol. %, or greaterthan or equal to 0.3 mol. % and less than or equal to 20.0 mol. %.

In some other embodiments, the glass composition may have a sum ofBi₂O₃+Cu₂O+CuO less than or equal to 1.0 mol. % or less than or equal to0.5 mol. %. In some more embodiments, the glass composition may have asum of Bi₂O₃+Cu₂O+CuO greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. %, or greater than or equal to 0.0 mol. % and lessthan or equal to 0.5 mol. %.

In some other embodiments, the glass composition may have a sum ofCu+Co+Cr+Ni less than or equal to 0.1 mol. % less than or equal to 0.10mol. % or less than or equal to 0.05 mol. %. In some more embodiments,the glass composition may have a sum of Cu+Co+Cr+Ni greater than orequal to 0.0 mol. % and less than or equal to 0.1 mol. %, greater thanor equal to 0.0 mol. % and less than or equal to 0.10 mol. %, or greaterthan or equal to 0.0 mol. % and less than or equal to 0.05 mol. %.

In some other embodiments, the glass composition may have a sum ofCu+Co+Ni+Cr+V+Bi less than or equal to 0.1 mol. % less than or equal to0.10 mol. % or less than or equal to 0.05 mol. %. In some moreembodiments, the glass composition may have a sum of Cu+Co+Ni+Cr+V+Bigreater than or equal to 0.0 mol. % and less than or equal to 0.1 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 0.05mol. %, greater than or equal to 0.0 mol. % and less than or equal to0.10 mol. %.

In some other embodiments, the glass composition may have a sum ofK₂O+Rb₂O+Cs₂O less than or equal to 3.0 mol. %, less than or equal to2.0 mol. %, or less than or equal to 1.0 mol. %. In some moreembodiments, the glass composition may have a sum of K₂O+Rb₂O+Cs₂Ogreater than or equal to 0.0 mol. % and less than or equal to 3.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 2.0mol. %, or greater than or equal to 0.0 mol. % and less than or equal to1.0 mol. %.

In some embodiments, the glass composition may have a sum ofLa₂O₃+CeO₂+Ce₂O₃ greater than or equal to 0.0 mol. %, greater than orequal to 0.5 mol. %, or greater than or equal to 10.0 mol. %. In someother embodiments, the glass composition may have a sum ofLa₂O₃+CeO₂+Ce₂O₃ less than or equal to 15.0 mol. % or less than or equalto 10.0 mol. %. In some more embodiments, the glass composition may havea sum of La₂O₃+CeO₂+Ce₂O₃ greater than or equal to 0.5 mol. % and lessthan or equal to 15.0 mol. %, greater than or equal to 0.0 mol. % andless than or equal to 15.0 mol. %, or greater than or equal to 0.0 mol.% and less than or equal to 10.0 mol. %, or greater than or equal to 0.5mol. % and less than or equal to 10.0 mol. %.

In some embodiments, the glass composition may have a sum of Li₂O+Na₂Ogreater than or equal to 0.0 mol. %, greater than or equal to 0.5 mol.%, greater than or equal to 2.0 mol. %, or greater than or equal to 5.0mol. %. In some other embodiments, the glass composition may have a sumof Li₂O+Na₂O less than or equal to 8.0 mol. % or less than or equal to5.0 mol. %. In some more embodiments, the glass composition may have asum of Li₂O+Na₂O greater than or equal to 0.0 mol. % and less than orequal to 8.0 mol. %, or greater than or equal to 0.0 mol. % and lessthan or equal to 5.0 mol. %, greater than or equal to 0.5 mol. % andless than or equal to 8.0 mol. %, or greater than or equal to 0.5 mol. %and less than or equal to 5.0 mol. %, greater than or equal to 2.0 mol.% and less than or equal to 8.0 mol. %, or greater than or equal to 2.0mol. % and less than or equal to 5.0 mol. %.

In some embodiments, the glass composition may have a sum ofLi₂O+Na₂O+MgO+CaO greater than or equal to 0.0 mol. %, greater than orequal to 0.5 mol. %, or greater than or equal to 10.0 mol. %. In someother embodiments, the glass composition may have a sum ofLi₂O+Na₂O+MgO+CaO less than or equal to 17.0 mol. % or less than orequal to 10.0 mol. %. In some more embodiments, the glass compositionmay have a sum of Li₂O+Na₂O+MgO+CaO greater than or equal to 0.5 mol. %and less than or equal to 17.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 17.0 mol. %, or greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, or greater than or equalto 0.5 mol. % and less than or equal to 10.0 mol. %.

In some embodiments, the glass composition may have a sum ofMgO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂ greater than or equal to 0.0 mol. %,greater than or equal to 0.5 mol. %, greater than or equal to 4.0 mol.%, or greater than or equal to 10.0 mol. %. In some other embodiments,the glass composition may have a sum ofMgO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂ less than or equal to 17.0 mol. % orless than or equal to 10.0 mol. %. In some more embodiments, the glasscomposition may have a sum of MgO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂greater than or equal to 0.0 mol. % and less than or equal to 17.0 mol.%, or greater than or equal to 0.0 mol. % and less than or equal to 10.0mol. %, greater than or equal to 0.5 mol. % and less than or equal to17.0 mol. %, or greater than or equal to 0.5 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 4.0 mol. % and less thanor equal to 17.0 mol. %, or greater than or equal to 4.0 mol. % and lessthan or equal to 10.0 mol. %.

In some embodiments, the glass composition may have a sum ofNa₂O+K₂O+BaO greater than or equal to 0.0 mol. %, or greater than orequal to 5.0 mol. %. In some other embodiments, the glass compositionmay have a sum of Na₂O+K₂O+BaO less than or equal to 10.0 mol. % or lessthan or equal to 5.0 mol. %. In some more embodiments, the glasscomposition may have a sum of Na₂O+K₂O+BaO greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, or greater than or equalto 0.0 mol. % and less than or equal to 5.0 mol. %.

In some embodiments, the glass composition may have a sum ofP₂O₅+Al₂O₃+B₂O₃+Li₂O+Na₂O+MgO+CaO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂greater than or equal to 0.0 mol. %, or greater than or equal to 50.0mol. %. In some other embodiments, the glass composition may have a sumof P₂O₅+Al₂O₃+B₂O₃+Li₂O+Na₂O+MgO+CaO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂less than or equal to 100 mol. % or less than or equal to 50.0 mol. %.In some more embodiments, the glass composition may have a sum ofP₂O₅+Al₂O₃+B₂O₃+Li₂O+Na₂O+MgO+CaO+TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂greater than or equal to 0.0 mol. % and less than or equal to 100 mol.%, or greater than or equal to 0.0 mol. % and less than or equal to 50.0mol. %.

In some embodiments, the glass composition may have a sum of P₂O₅+B₂O₃greater than or equal to 0.0 mol. %, greater than or equal to 15.0 mol.%, greater than or equal to 50.0 mol. %, or greater than or equal to60.0 mol. %. In some other embodiments, the glass composition may have asum of P₂O₅+B₂O₃ less than or equal to 75.0 mol. %, less than or equalto 73.0 mol. %, or less than or equal to 50.0 mol. %. In some moreembodiments, the glass composition may have a sum of P₂O₅+B₂O₃ greaterthan or equal to 15.0 mol. % and less than or equal to 75.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 75.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 73.0mol. %, or greater than or equal to 0.0 mol. % and less than or equal to50.0 mol. %, greater than or equal to 15.0 mol. % and less than or equalto 73.0 mol. %, or greater than or equal to 15.0 mol. % and less than orequal to 50.0 mol. %, greater than or equal to 50.0 mol. % and less thanor equal to 75.0 mol. %, or greater than or equal to 50.0 mol. % andless than or equal to 73.0 mol. %.

In some other embodiments, the glass composition may have a sum ofK₂O+Rb₂O+Cs₂O less than or equal to 3.0 mol. %, less than or equal to2.0 mol. %, or less than or equal to 1.0 mol. %. In some moreembodiments, the glass composition may have a K₂O+Rb₂O+Cs₂O greater thanor equal to 0.0 mol. % and less than or equal to 3.0 mol. %, greaterthan or equal to 0.0 mol. % and less than or equal to 2.0 mol. %, orgreater than or equal to 0.0 mol. % and less than or equal to 1.0 mol.%.

In some embodiments, the glass composition may have a sum ofK₂O+Rb₂O+Cs₂O greater than or equal to 0.0 mol. %, or greater than orequal to 5.0 mol. %. In some other embodiments, the glass compositionmay have a sum of K₂O+Rb₂O+Cs₂O less than or equal to 9.5 mol. % or lessthan or equal to 5.0 mol. %. In some more embodiments, the glasscomposition may have a K₂O+Rb₂O+Cs₂O greater than or equal to 0.0 mol. %and less than or equal to 9.5 mol. %, or greater than or equal to 0.0mol. % and less than or equal to 5.0 mol. %.

In some other embodiments, the glass composition may have a sum ofZnO+CuO+Cu₂O less than or equal to 0.5 mol. % or less than or equal to0.25 mol. %. In some more embodiments, the glass composition may have aZnO+CuO+Cu₂O greater than or equal to 0.0 mol. % and less than or equalto 0.5 mol. %, or greater than or equal to 0.0 mol. % and less than orequal to 0.25 mol. %.

In some embodiments, the glass composition may have a sum of R₂O+ROgreater than or equal to 0.0 mol. %, greater than or equal to 0.5 mol.%, greater than or equal to 1.0 mol. %, greater than or equal to 8.0mol. %, greater than or equal to 10.0 mol. %, or greater than or equalto 20.0 mol. %. In some other embodiments, the glass composition mayhave a sum of R₂O+RO less than or equal to 28.0 mol. %, less than orequal to 20.0 mol. %, less than or equal to 15.0 mol. %, less than orequal to 12.0 mol. %, or less than or equal to 10.0 mol. %. In some moreembodiments, the glass composition may have a sum of R₂O+RO greater thanor equal to 0.0 mol. % and less than or equal to 28.0 mol. %, greaterthan or equal to 1.0 mol. % and less than or equal to 15.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 15.0mol. %, greater than or equal to 0.0 mol. % and less than or equal to12.0 mol. %, or greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. %, greater than or equal to 1.0 mol. % and less thanor equal to 28.0 mol. %, greater than or equal to 1.0 mol. % and lessthan or equal to 20.0 mol. %, greater than or equal to 1.0 mol. % andless than or equal to 12.0 mol. %, or greater than or equal to 1.0 mol.% and less than or equal to 10.0 mol. %, greater than or equal to 8.0mol. % and less than or equal to 28.0 mol. %, greater than or equal to8.0 mol. % and less than or equal to 20.0 mol. %, greater than or equalto 8.0 mol. % and less than or equal to 15.0 mol. %, greater than orequal to 8.0 mol. % and less than or equal to 12.0 mol. %, or greaterthan or equal to 8.0 mol. % and less than or equal to 10.0 mol. %,greater than or equal to 10.0 mol. % and less than or equal to 28.0 mol.%, greater than or equal to 10.0 mol. % and less than or equal to 20.0mol. %, greater than or equal to 10.0 mol. % and less than or equal to15.0 mol. %, or greater than or equal to 10.0 mol. % and less than orequal to 12.0 mol. %.

In some embodiments, the glass composition may have a sum of R₂O+RO+B₂O₃greater than or equal to 0.0 mol. %, greater than or equal to 0.5 mol.%, greater than or equal to 10.0 mol. %, greater than or equal to 12.0mol. %, or greater than or equal to 20.0 mol. %. In some otherembodiments, the glass composition may have a sum of R₂O+RO+B₂O₃ lessthan or equal to 22.0 mol. %, less than or equal to 20.0 mol. %, or lessthan or equal to 10.0 mol. %. In some more embodiments, the glasscomposition may have a sum of R₂O+RO+B₂O₃ greater than or equal to 0.0mol. % and less than or equal to 22.0 mol. %, greater than or equal to0.0 mol. % and less than or equal to 20.0 mol. %, or greater than orequal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater thanor equal to 0.5 mol. % and less than or equal to 22.0 mol. %, greaterthan or equal to 0.5 mol. % and less than or equal to 20.0 mol. %, orgreater than or equal to 0.5 mol. % and less than or equal to 10.0 mol.%, greater than or equal to 10.0 mol. % and less than or equal to 22.0mol. %, or greater than or equal to 10.0 mol. % and less than or equalto 20.0 mol. %, greater than or equal to 12.0 mol. % and less than orequal to 22.0 mol. %, or greater than or equal to 12.0 mol. % and lessthan or equal to 20.0 mol. %.

In some embodiments, the glass composition may have a sum ofR₂O+RO+SnO₂+MnO₂ greater than or equal to 0.0 mol. %, greater than orequal to 8.0 mol. %, or greater than or equal to 10.0 mol. %. In someother embodiments, the glass composition may have a sum ofR₂O+RO+SnO₂+MnO₂ less than or equal to 15.0 mol. %, less than or equalto 12.0 mol. %, or less than or equal to 10.0 mol. %. In some moreembodiments, the glass composition may have a sum of R₂O+RO+SnO₂+MnO₂greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol.%, greater than or equal to 0.0 mol. % and less than or equal to 12.0mol. %, or greater than or equal to 0.0 mol. % and less than or equal to10.0 mol. %, greater than or equal to 8.0 mol. % and less than or equalto 15.0 mol. %, greater than or equal to 8.0 mol. % and less than orequal to 12.0 mol. %, or greater than or equal to 8.0 mol. % and lessthan or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % andless than or equal to 15.0 mol. %, or greater than or equal to 10.0 mol.% and less than or equal to 12.0 mol. %.

In some other embodiments, the glass composition may have a sum ofTeO₂+GeO₂ less than or equal to 5.0 mol. %, less than or equal to 3.0mol. %, or less than or equal to 2.5 mol. %. In some more embodiments,the glass composition may have a sum of TeO₂+GeO₂ greater than or equalto 0.0 mol. % and less than or equal to 5.0 mol. %, greater than orequal to 0.0 mol. % and less than or equal to 3.0 mol. %, or greaterthan or equal to 0.0 mol. % and less than or equal to 2.5 mol. %.

In some embodiments, the glass composition may have a sum ofTiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂ greater than or equal to 0.0 mol. %,greater than or equal to 0.5 mol. %, or greater than or equal to 10.0mol. %. In some other embodiments, the glass composition may have a sumof TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂ less than or equal to 20.0 mol. %,less than or equal to 13.0 mol. %, or less than or equal to 10.0 mol. %.In some more embodiments, the glass composition may have a sum ofTiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂ greater than or equal to 0.5 mol. % andless than or equal to 20.0 mol. %, greater than or equal to 0.0 mol. %and less than or equal to 20.0 mol. %, greater than or equal to 0.0 mol.% and less than or equal to 13.0 mol. %, or greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. %, greater than or equal to0.5 mol. % and less than or equal to 13.0 mol. %, or greater than orequal to 0.5 mol. % and less than or equal to 10.0 mol. %, greater thanor equal to 10.0 mol. % and less than or equal to 20.0 mol. %, orgreater than or equal to 10.0 mol. % and less than or equal to 13.0 mol.%.

In some embodiments, the glass composition may have a sum of TiO₂+ZrO₂greater than or equal to 0.0 mol. %, greater than or equal to 0.25 mol.%, or greater than or equal to 20.0 mol. %. In some other embodiments,the glass composition may have a sum of TiO₂+ZrO₂ less than or equal to40.0 mol. % or less than or equal to 20.0 mol. %. In some moreembodiments, the glass composition may have a sum of TiO₂+ZrO₂ greaterthan or equal to 0.25 mol. % and less than or equal to 40.0 mol. %,greater than or equal to 0.0 mol. % and less than or equal to 40.0 mol.%, or greater than or equal to 0.0 mol. % and less than or equal to 20.0mol. %, or greater than or equal to 0.25 mol. % and less than or equalto 20.0 mol. %.

In some embodiments, the glass composition may have a value of3*Al₂O₃+R₂O+RO−P₂O₅ greater than or equal to −7 mol. %, greater than orequal to −5 mol. %, greater than or equal to −3 mol. %, or greater thanor equal to 2 mol. %. In some other embodiments, the glass compositionmay have a value of 3*Al₂O₃+R₂O+RO−P₂O₅ less than or equal to 2.1 mol.%, less than or equal to 2 mol. %, or less than or equal to −3 mol. %.In some more embodiments, the glass composition may have a3*Al₂O₃+R₂O+RO−P₂O₅ greater than or equal to −7 mol. % and less than orequal to 2.1 mol. %, greater than or equal to −7 mol. % and less than orequal to 2 mol. %, or greater than or equal to −7 mol. % and less thanor equal to −3 mol. %, greater than or equal to −5 mol. % and less thanor equal to 2.1 mol. %, greater than or equal to −5 mol. % and less thanor equal to 2 mol. %, or greater than or equal to −5 mol. % and lessthan or equal to −3 mol. %, greater than or equal to −3 mol. % and lessthan or equal to 2.1 mol. %, or greater than or equal to −3 mol. % andless than or equal to 2 mol. %.

In some embodiments, glass composition may have limitations forAl₂O₃−R₂O−RO. It was empirically found that when the content of aluminain the glass is low and/or the total content of divalent and monovalentmetal oxides is high, chemical durability may tend to decrease. In someembodiments, the glass composition may have a difference Al₂O₃−R₂O−ROgreater than or equal to 3.0 mol. %, greater than or equal to 7.95 mol.%, or greater than or equal to 8.0 mol. %. In some other embodiments,the glass composition may have a difference Al₂O₃−R₂O−RO less than orequal to 9.0 mol. % or less than or equal to 8.0 mol. %. In some moreembodiments, the glass composition may have a Al₂O₃−R₂O−RO greater thanor equal to 3.0 mol. % and less than or equal to 9.0 mol. %, or greaterthan or equal to 3.0 mol. % and less than or equal to 8.0 mol. %,greater than or equal to 7.95 mol. % and less than or equal to 9.0 mol.%.

In some embodiments, glass composition may have limitations for a ratio(La₂O₃+CeO₂+Ce₂O₃)/RE_(m)O_(n). Lanthanum and cerium oxides are thecheapest of the rare earth metal oxides. Accordingly, in the cases whenlow cost is demanded, it may be preferable to use these rare earth metaloxides. In some embodiments, the glass composition may have a ratio(La₂O₃+CeO₂+Ce₂O₃)/RE_(m)O_(n) [mol. %] greater than or equal to 0.000,or greater than or equal to 0.51.

In some embodiments, glass composition may have limitations for a ratio(Li₂O+Na₂O)/R₂O. Lithium and sodium oxides have a greater impact on theYoung's modulus than other monovalent metal oxides (such as K₂O, Cs₂O,Cu₂O, etc.). Accordingly, a high ratio (Li₂O+Na₂O)/R₂O is correlatedwith a higher impact of the monovalent metal oxides on the Young'smodulus. In some embodiments, the glass composition may have a ratio(Li₂O+Na₂O)/R₂O greater than or equal to 0.750, greater than or equal to0.850, or greater than or equal to 0.950. In some other embodiments, theglass composition may have a ratio (Li₂O+Na₂O)/R₂O less than or equal to1.000, less than or equal to 0.950, or less than or equal to 0.850. Insome more embodiments, the glass composition may have a ratio(Li₂O+Na₂O)/R₂O greater than or equal to 0.750 and less than or equal to1.000, greater than or equal to 0.750 and less than or equal to 0.950,or greater than or equal to 0.750 and less than or equal to 0.850,greater than or equal to 0.850 and less than or equal to 1.000, orgreater than or equal to 0.850 and less than or equal to 0.950.

In some embodiments, glass composition may have limitations for a ratioP₂O₅/(3*Al₂O₃+B₂O₃). It was empirically found that when the ratioP₂O₅/(3*Al₂O₃+B₂O₃) is close to unity, it is possible to reach highelastic modulus and adequate chemical durability, as well as to reducevolatilization of both P₂O₅ and B₂O₃ when melting. When the ratioP₂O₅/(3*Al₂O₃+B₂O₃) is low, chemical durability may tend to decrease.When the ratio P₂O₅/(3*Al₂O₃+B₂O₃) is high, P₂O₅ and B₂O₃ may volatilizewhen melting. Also, when the ratio P₂O₅/(3*Al₂O₃+B₂O₃) is significantlylower or higher than 1.0, it may also be difficult to reach high elasticmodulus. In some embodiments, the glass composition may have a ratioP₂O₅/(3*Al₂O₃+B₂O₃) mol. %/mol. % greater than or equal to 0.95, greaterthan or equal to 1.00, or greater than or equal to 1.15. In some otherembodiments, the glass composition may have a ratio P₂O₅/(3*Al₂O₃+B₂O₃)mol. % less than or equal to 1.30, less than or equal to 1.25, less thanor equal to 1.16, or less than or equal to 1.15. In some moreembodiments, the glass composition may have a ratio P₂O₅/(3*Al₂O₃+B₂O₃)mol. % greater than or equal to 0.95 and less than or equal to 1.20,greater than or equal to 0.95 and less than or equal to 1.30, greaterthan or equal to 0.95 and less than or equal to 1.16, or greater than orequal to 0.95 and less than or equal to 1.15, greater than or equal to1.00 and less than or equal to 1.30, greater than or equal to 1.00 andless than or equal to 1.20, greater than or equal to 1.00 and less thanor equal to 1.16, or greater than or equal to 1.00 and less than orequal to 1.15, greater than or equal to 1.15 and less than or equal to1.30, greater than or equal to 1.15 and less than or equal to 1.25.

In some embodiments, the Young's modulus E of the glass is from greaterthan or equal to 60 GPa to less than or equal to 120 GPa and all rangesand sub-ranges between the foregoing values. In some embodiments, theYoung's modulus E of the glass is greater than or equal to 60 GPa,greater than or equal to 70 GPa, greater than or equal to 74 GPa,greater than or equal to 75 GPa, greater than or equal to 80 GPa,greater than or equal to 85 GPa, greater than or equal to 105 GPa,greater than or equal to 110 GPa, or greater than or equal to 115 GPa.In some other embodiments, the Young's modulus E of the glass is lessthan or equal to 120 GPa, less than or equal to 115 GPa, less than orequal to 110 GPa, less than or equal to 105 GPa, less than or equal to85 GPa, less than or equal to 80 GPa, or less than or equal to 70 GPa.In some more embodiments, the Young's modulus E of the glass is greaterthan or equal to 60 GPa and less than or equal to 120 GPa, greater thanor equal to 70 GPa and less than or equal to 80 GPa, greater than orequal to 75 GPa and less than or equal to 120 GPa, greater than or equalto 75 GPa and less than or equal to 80 GPa, greater than or equal to 85GPa and less than or equal to 105 GPa.

In some embodiments, the logarithm of liquidus viscosity Log(η_(Uq),[P]) of the glass is greater than or equal to 2.

In some embodiments, the glass may have the average linear thermalexpansion coefficient of glass in the range 20-300° C. α₂₀₋₃₀₀×10⁷ fromgreater than or equal to 60.0 K⁻¹ to less than or equal to 70.0 K⁻¹, andall ranges and sub-ranges between the foregoing values. In someembodiments, the average linear thermal expansion coefficient of theglass in the range 20-300° C. α₂₀₋₃₀₀×10⁷ is greater than or equal to60.0 K⁻¹, greater than or equal to 61.0 K⁻¹, greater than or equal to63.0 K⁻¹, greater than or equal to 65.0 K⁻¹, greater than or equal to67.0 K⁻¹, greater than or equal to 68.0 K⁻¹, or greater than or equal to69.0 K⁻¹. In some other embodiments, the average linear thermalexpansion coefficient of the glass in the range 20-300° C. α₂₀₋₃₀₀×10⁷is less than or equal to 70.0 K⁻¹, less than or equal to 69.0 K⁻¹, lessthan or equal to 68.0 K⁻¹, less than or equal to 67.0 K⁻¹, less than orequal to 65.0 K⁻¹, or less than or equal to 61.0 K⁻¹. In some moreembodiments, the average linear thermal expansion coefficient of theglass in the range 20-300° C. α₂₀₋₃₀₀×10⁷ is greater than or equal to60.0 K⁻¹ and less than or equal to 70.0 K⁻¹, greater than or equal to63.0 K⁻¹ and less than or equal to 67.0 K⁻¹, greater than or equal to60.0 K⁻¹ and less than or equal to 61.0 K⁻¹, greater than or equal to61.0 K⁻¹ and less than or equal to 70.0 K⁻¹, greater than or equal to61.0 K⁻¹, and less than or equal to 65.0 K⁻¹, greater than or equal to63.0 K⁻¹, and less than or equal to 70.0 K⁻¹, greater than or equal to63.0 K⁻¹, and less than or equal to 65.0 K⁻¹, greater than or equal to65.0 K⁻¹, and less than or equal to 70.0 K⁻¹, greater than or equal to65.0 K⁻¹, and less than or equal to 67.0 K⁻¹, greater than or equal to67.0 K⁻¹, and less than or equal to 70.0 K⁻¹, greater than or equal to67.0 K⁻¹ and less than or equal to 68.0 K⁻¹.

In some embodiments, the glass may have the Abbe number v_(d) greaterthan or equal to 60, or greater than or equal to 65, or greater than orequal to 68, or greater than or equal to 70, or greater than or equal to71.

The chemical durability of samples of glasses described herein wasassessed with the acid durability tests and base durability testsdescribed below. To prepare the glass samples for each of the tests, theglass samples were (1) rinsed under distilled water (16 MΩ resistance)for 5 minutes while squeezing the water from Tygon tubing to provide ashower-like rinse; (2) ultrasonicated (50/60 Hz frequency) at 60° C. to65° C. in a 4% Semiclean Detergent bath for one minute; (3) rinsed under16 MΩ distilled water for 5 minutes while squeezing the water from Tygontubing to provide a shower-like rinse; and (4) rinsed in a cascading 18MΩ distilled water bath for 5 minutes. The glass samples were thentransferred onto glass racks on stainless steel trays and dried in a110° C. oven for an hour, and placed in a desiccator until tested. Aciddurability tests were done in Pyrex tubes in a hot water bath and basedurability tests were done in platinum tubes in a hot water bath. Theresults of the acid and base durability tests are reported as the massdifference of the sample before and after the test divided by theinitial surface area of the sample. The results are reported as the massdifference per unit area and are expressed in units of mg/cm². A smallmass difference per unit area reflects a low loss of mass and signifieshigh durability.

Durability to acids was characterized in some embodiments according tothe standard DIN12116. The measured quantity, specified in Table 6 belowas “HCl[DIN12116]”, is the mass difference per unit area determinedaccording to the procedure specified in standard DIN12116.

Alternatively, for some Exemplary Glasses the durability to acids wastested by immersion of glass samples with dimensions of about 2×2″ in asolution of 5 wt % HCl at 95° C. for 24 hours. The measured quantity,specified in Table 6 below as “Durability HCl 5% w/95 C/24 h”, is themass difference per unit area according to this acid durability test.

Durability to bases was characterized in some embodiments according tothe standard ISO695. The measured quantity, specified in Table 6 belowas “NaOH[ISO695]”, is the mass difference per unit area according to theprocedure specified in the standard ISO695.

Alternatively, for some Exemplary Glasses the durability to bases wastested by exposure glass samples with dimensions of about 2×2” in asolution of 5 wt % NaOH at 95° C. for 1 hour. The measured quantity,specified in Table 6 below as “Durability NaOH 5% w, 95 C, 1 hr”, is themass difference per unit area according to this base durability test.

When testing the durability of glass samples to vapor hydrofluoric acid(vHF or vHF durability test), the glass samples were wiped with ethanolor IPA (isopropyl alcohol), weighed, then placed in Teflon mesh basketsand placed in a closed vessel above 250 ml of 5 wt % HF solution held ata temperature of 50° C. The glass samples were exposed to vapor HF fromthe solution for 1 hour, then removed from the vessel and placed into 16MΩ DI water to quench. The glass samples were then removed from thebaskets and rinsed first under 16 MΩ DI water, then under 18 MΩ DIwater. After rinsing, the glass samples were placed on a glass racksituated on a stainless steel tray and set in a 110° C. oven for about30 min. Samples were cooled, then reweighed and visually evaluated forthe surface damage. The result of the vHF durability test is reported asthe mass difference of the sample before and after exposure to vHFdivided by the initial surface area of the sample (referred to in Table6 below as “vHF loss”), expressed in mg/cm², according to this test.

After the vHF test, appearance of surface was evaluated in terms ofvisually observed surface damage and gloss. This characteristic isspecified in Table 6 below as “vHF appearance”, where “OK” means novisible surface damage.

Weathering tests were conducted to evaluate the durability of glasssamples to hot wet air. In the weathering test, glass sheets of about30×30 mm size were exposed to air having a relative humidity of 85% at85° C. for 144 hours. The mass difference per unit area of the glasssamples after exposure to the humid air was determined. The measuredquantity, specified in Table 6 below as “Weathering—85° C./85% RH”, isthe mass difference of the sample before and after exposure to the humidair divided by the initial surface area of the sample, expressed inunits of mg/cm². The surface damage after the weathering test wasvisually characterized.

Batch index I_(B) is a quantity calculated by the following formula (I):

I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅,  (I)

where R₂O is total sum of monovalent metal oxides, RO is total sum ofdivalent metal oxides, RE₂O₃ is total sum of rare earth metal oxides inthe “+3” redox state, and chemical formulas mean the amounts ofcorresponding components in the glass composition.

Batch index I_(B) determines the viability of batching all P₂O₅ fromsolid starting materials, such as monovalent and divalent metalmetaphosphates (M_(x)O*P₂O₅, where “M” refers to a metal cation, and xis 1 or 2, depending on the redox state of the metal cation M), aluminummetaphosphate (Al₂O₃*3P₂O₅), boron phosphate (B₂O₃*P₂O₅) and rare earthmetals metaphosphates (RE₂O₃*3P₂O₅, where “RE” refers to a rare earthmetal cation). Accordingly, the coefficients in the formula (I)correspond to the stoichiometric factors of P₂O₅ in the indicated solidphosphate starting materials. When the batch index I_(B) is zero orpositive then it is expected to be possible to batch P₂O₅ from the solidstarting materials noted in this paragraph. This simplifies the meltingprocess and reduces its cost.

Young's modulus E is a property of glass that can be predicted from theglass composition. A linear regression analysis of the Exemplary Glassesof the present disclosure in the EXAMPLES section below and other glasscompositions reported in the literature was performed to determine anequation that can predict the composition dependence of the Young'smodulus E.

The training dataset of glass compositions satisfying the compositionallimitations specified in Table 1 below and having measured values of theYoung's modulus E, about 100 glass compositions, was randomly selectedfrom literature data presented in the publicly available SciGlassInformation System database and from the Exemplary Glasses from theembodiments presented herein. The linear regression analysis on theabove-specified dataset was used to determine the formula (II) for theparameter P_(E) that predicts the Young's modulus E. Outliers in thedataset were excluded to improve the accuracy of the result. Theresulting formula (II) is presented below and summarized in Table 2.Another subset of glass compositions satisfying the compositionallimitations of Table 1 was used as a validation set to evaluate theability to interpolate within the compositional limitations of Table 1and was used to establish the standard deviation specified in Table 2for the parameter P_(E). An external dataset of prior art glasscompositions, also randomly selected from the SciGlass InformationSystem database, was used to evaluate the ability to predict theproperties outside of the compositional limits of Table 1 with areasonable accuracy. Multiple iterations of this process were performedin order to determine the best formula for predicting the Young'smodulus E. Formula (II) is the result of the analysis.

The data for the Comparative Glass compositions used in the linearregression modeling, including the training dataset, validation datasetand external dataset were obtained from the publically availableSciGlass Information System database. Formula (II) below were obtainedfrom the linear regression analysis and defines a parameter P_(E) usedto predict the Young's modulus E of the glasses:

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70.  (II)

In Formula (II) and Tables 1 and 2, P_(E) is a parameter that predictsthe Young's modulus [GPa], calculated from the components of the glasscomposition expressed in mol. %. In Table 1, RE_(m)O_(n) is a total sumof rare earth metal oxides, R₂O is a total sum of monovalent metaloxides, RO is a total sum of divalent metal oxides and R_(m)O_(n) is atotal sum of all oxides.

In Formula (II), each component of the glass composition is listed interms of its chemical formula, where the chemical formula refers to theconcentration of the component expressed in mol. %. For example, forpurposes of Formula (II), P₂O₅ refers to the concentration of P₂O₅,expressed in mol. %, in the glass composition. It is understood that notall components listed in Formula (II) are necessarily present in aparticular glass composition and that Formula (II) is equally valid forglass compositions that contain less than all of the components listedin the formula. It is further understood that Formula (II) is also validfor glass compositions within the scope and claims of the presentdisclosure that contain components in addition to the components listedin the formulas. If a component listed in Formula (II) is absent in aparticular glass composition, the concentration of the component in theglass composition is 0 mol. % and the contribution of the component tothe value calculated from the formulas is zero.

TABLE 1 Composition Space Used for Modeling Property E, GPa Componentlimits Min, mol. % Max, mol. % P₂O₅ + B₂O₃ 30 75 P₂O₅ 20 75 Al₂O₃ 0 20B₂O₃ 0 35 TiO₂ 0 20 Li₂O 0 20 Y₂O₃ 0 20 La₂O₃ 0 20 CeO₂ 0 20 Nb₂O₅ 0 20Ta₂O₅ 0 20 WO₃ 0 20 RE_(m)O_(n) 0 20 Na₂O + K₂O 0 20 Rb₂O + Cs₂O 0 10R₂O + RO 0 25 R_(m)O_(n) 99 Not limited Other species 0 Not limited

TABLE 2 Property prediction model Com- Prop- Abbre- PredictingRegression position Standard erty viation Unit Parameter Formula UnitDeviation Young's E GPa P_(E) Formula (II) Mol. % 10 modulus

FIG. 1 is a plot of the parameter P_(E) calculated by Formula (II) as afunction of the measured Young's modulus E for some Comparative Glasses(“Comp. Glasses”) taken from the literature and some Exemplary Glasses(“Ex. Glasses”). As illustrated by the data in FIG. 1 , thecompositional dependence of the parameter P_(E) had a deviation within arange of ±10 GPa of the measured Young's modulus E for the majority ofglasses. This deviation corresponds to the standard deviation specifiedin Table 2.

In the expression for P_(E), the term“RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂” refers to the residual amount of therare earth metal oxides after deducting lanthanum, yttrium and ceriumoxides that are accounted individually. Accordingly, this termapproximately considers the impacts of the rare earth metal oxides otherthan lanthanum, yttrium and cerium oxides on the Young's modulus E.

The term “max(0,min(B₂O₃, P₂O₅−3*Al₂O₃−(3*RE_(m)O_(n)+R₂O+MgO+CaO)))”describes the anomalously high Young's modulus observed in the data setfor some aluminoborophosphate glasses with high content of P₂O₅. Theanomaly was observed when the content of P₂O₅ in the glass compositionexceeded the total amount of P₂O₅ that, according to stoichiometry, canbe bound in metaphosphates of alumina (Al₂O₃*3P₂O₅), rare earth metals(RE₂O₃*3P₂O₅), monovalent metals (R₂O*P₂O₅) and magnesium and calciumoxides (RO*P₂O₅, where R═Mg or Ca).

Not referring to any specific theory, it is believed that the residualamount of P₂O₅, which can be calculated asP₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO), can be bound with B₂O₃,forming some structural units containing only bridging oxygen atoms,where boron and phosphorus atoms are fourfold-coordinated like those incrystalline boron phosphate (BPO₄). Then, in the case when thedifference P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO) is positive, it isbelieved that alumina is also bounded with P₂O₅.

In the case when the value of P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO)exceeds the amount of B₂O₃, it is believed that the effective amount ofP₂O₅ is equal to the content of B₂O₃ in the glass composition.Accordingly, the quantity “min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))” works both in cases when theglass composition has an excess of P₂O₅ and an excess of B₂O₃.

In turn, in the case when the content of P₂O₅ in the glass compositionis insufficient to bind alumina, rare earth metals, monovalent metalsand divalent metals in their metaphosphates (corresponding to negativevalues of min(B₂O₃, P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO)), it isbelieved that binding of P₂O₅ with B₂O₃ does not take place, which meansthat the anomalous effect does not occur. Accordingly, the term“max(0,min(B₂O₃, P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO)))” generalizesthe above-presented expression to the case when this quantity is equalto zero.

According to some data (see, for example, Ohkawa H., Min K. H., AkiyamaR., Yamamoto K., Sugimoto N., Refractive index behavior in phosphateglass from the viewpoint of B₃ ⁺ and Al₃ ⁺ coordination., J. Non-Cryst.Solids, 2008, vol. 354, No. 2-9, p. 90-93), the glasses containingsimultaneously P₂O₅, Al₂O₃, B₂O₃ and some monovalent and/or divalentmetal oxides, the composition dependences of physical properties maybecome nonlinear because of coordination changes of cations. In turn,this may cause variable (including sign-changed) deviations of predictedvalues of those properties from the measured values. The above-describednonlinear term is assumed to approximately consider the effects of thementioned coordination changes on the Young's modulus of glasses and,therefore, reduce the error of prediction for this property.

Table 3 identifies the combination of components and their respectiveamounts according to some embodiments of the present disclosure. TheExemplary Glasses A in Table 3 may include additional componentsaccording to any aspects of the present disclosure as described herein.

TABLE 3 Exemplary Glasses A Composition Amount (mol. %) B₂O₃ 0.3 to 50.0mol. % P₂O₅ 0.0 to 75.0 mol. % MgO 0.5 to 15.0 mol. % Al₂O₃ 0.0 to 30.0mol. % Sum of (P₂O₅ + B₂O₃) 15.0 to 75.0 mol. % Total sum of monovalentmetal oxides R₂O 0.3 to 15.0 mol. % Sum of (R₂O + RO + SnO₂ + MnO₂) 0.8to 15.0 mol. % Sum of (TeO₂ + GeO₂) 0.0 to 5.0 mol. %

Exemplary Glasses A according to embodiments of the present disclosuremay optionally fluorine (F) in an amount 0.0 to 0.5 at. %.

According to some embodiments of the present disclosure, ExemplaryGlasses A may also satisfy the following condition:

(Li₂O+Na₂O)/R₂O [mol. %]≥0.75,

where chemical formulas refer to the amounts of the components in theglass composition, expressed in mol. %.

Table 4 identifies the combination of components and their respectiveamounts according to some embodiments of the present disclosure. TheExemplary Glasses B in Table 4 may include additional componentsaccording to any aspects of the present disclosure as described herein.

TABLE 4 Exemplary Glasses B Composition Amount (mol. %) P₂O₅ 40.0 to75.0 mol. % B₂O₃ 0.5 to 10.5 mol. % Al₂O₃ 0.0 to 25.0 mol. % Sum of(R₂O + RO) 2 0.5 mol. % Sum of (K₂O + Rb₂O + Cs₂O) 0.0 to 9.5 mol. %

Exemplary Glasses B according to embodiments of the present disclosuremay also optionally contain fluorine (F) in an amount 0.0 to 5.0 at. %.

Exemplary Glasses B according to embodiments of the present disclosuremay also satisfy the following condition:

P₂O₅/(3*Al₂O₃+B₂O₃) [mol. %]≤1.3,

where chemical formulas refer to the amounts of the components in theglass composition, expressed in mol. %.

According to some embodiments of the present disclosure, ExemplaryGlasses B may also satisfy the following condition:

3*Al₂O₃+R₂O+RO−P₂O₅ [mol. %]≥−7.0,

where chemical formulas refer to the amounts of components in glass,expressed in mol. %.

According to some embodiments of the present disclosure, ExemplaryGlasses B may also satisfy the following condition:

Al₂O₃−R₂O−RO [mol. %]≥7.95,

where chemical formulas refer to the amounts of components in glass,expressed in mol. %.

Table 5 identifies the combination of components and their respectiveamounts according to some embodiments of the present disclosure. TheExemplary Glasses C in Table 5 may include additional componentsaccording to any aspects of the present disclosure as described herein.

TABLE 5 Exemplary Glasses C Composition Amount (mol. %) P₂O₅ 40.0 to75.0 mol. % Al₂O₃ 3.0 to 30.0 mol. % Li₂O 0.0 to 20.0 mol. % ZnO 0.0 to15.0 mol. % B₂O₃ 0.0 to 15.0 mol. % Sum of 0.5 to 20.0 mol. % (TiO₂ +La₂O₃ + Y₂O₃ + Ce₂O₃ + CeO₂ + ZrO₂) Sum of (R₂O + RO + B₂O₃) >0.5 mol. %Sum of (R₂O + RO) 0.0 to 28.0 mol. % Total sum of divalent metal oxidesRO 0.0 to 20.0 mol. %

Exemplary Glasses C according to embodiments of the present disclosuremay optionally contain fluorine (F) in an amount 0.0 to 1.0 at. %.

According to some embodiments of the present disclosure, ExemplaryGlasses C may also have a Young's modulus E [GPa] of greater than orequal to 75.

Examples

The following examples describe various features and advantages providedby the disclosure, and are in no way intended to limit the invention andappended claims.

To prepare the glass samples for some exemplary glasses of the presentdisclosure, about 15 grams of each sample (content of target species wasmore than 99.99 wt %) was melted from batch raw materials at atemperature of 1300-1500° C. in platinum or platinum-rhodium crucibles(Pt:Rh=80:20) for 1 hour. Two controlled cooling conditions wereapplied. In the first condition (referred to as “15 min test” or “15 mindevit test”), the cooling conditions were controlled so that it tookabout 15 min for the samples to cool from 1100° C. to 500° C. in airinside a furnace. In the second condition (referred to as “2.5 min test”or “2.5 min devit test”), the cooling conditions were controlled so thatit took about 2.5 min for the samples to cool from 1100° C. to 500° C.in air inside a furnace. Temperature readings were obtained by directreading of the furnace temperature or using an IR camera reading withcalibration scaling. The first condition (15 min test) approximatelycorresponds to a cooling rate of up to 300° C./min at a temperature of1000° C. and the second test approximately corresponds to a cooling rateof up to 600° C./min at 1000° C. (the temperature of 1000° C.corresponds approximately to the temperature at which the cooling ratewas expected to approach a maximum). When the temperature is lower, thecooling rate also decreases significantly. Typical schedules of thefirst and second cooling regimes are shown in FIG. 2 . For thesesamples, observations referred to as “15-min devit test” and “2.5-mindevit test” are specified in Table 6 below; the observation “1” is usedto denote that a glass composition passed the indicated devit test,where a composition is deemed to have passed the indicated devit test ifa melt of the composition forms a glass free of crystals visible underan optical microscope under magnification from 100× to 500×. Theobservation “0” is used to denote that a glass composition failed theindicated devit test.

No direct chemical analysis of some of the glass samples was performedbecause chemical analysis was performed for similar samples prepared inindependent meltings by XRF method (X-ray fluorescence—for all oxides,except for B₂O₃ and Li₂O), by ICP method (inductively coupled plasmamass spectrometry—for B₂O₃) and by FES method (flame emissionspectrometry—for Li₂O). These analyses gave deviations from the batchedcompositions within ±1.0-1.5 mass % for the major components such asAl₂O₃ which is equivalent to about 1 mol %.

To prepare other glass samples for exemplary glasses of the presentdisclosure, unless otherwise specified, a one kilogram batch wasprepared in a pure platinum crucible. The crucible was placed in afurnace set at a temperature of 1300-1500° C. for 4 hours. The glassmelt was then poured on a steel table and annealed at temperature closeto T_(g) for an hour. The annealed glasses were inspected under anoptical microscope to check for crystallization and were found to becrystal free. The glass quality observed under the optical microscopewas good and the samples were free of striae and bubbles. The sampleswere analyzed by XRF and FES methods.

Table 6 summarizes representative glass compositions in accordance withthe present disclosure and selected properties of each. In Table 6,T_(200 P) refers to the temperature at which the glass has a viscosityof 200 Poise and T_(x) refers to the temperature corresponding to theonset of crystallization.

TABLE 6 Exemplary Glass Compositions Exemplary Glass 1 2 3 4Composition-mol. % P₂O₅ mol. % 62.19 58.97 57.07 64.97 Al₂O₃ mol. %17.48 17.53 15.84 29.99 B₂O₃ mol. % 4.85 7.60 2.90 0 La₂O₃ mol. % 2.915.91 5.84 0 Li₂O mol. % 7.74 7.77 7.69 2.52 TiO₂ mol. % 0 0 0 2.50 MgOmol. % 0 1.16 0.93 0 Na₂O mol. % 0.95 1.03 0.0223 0 CeO₂ mol. % 0.970.0377 1.95 0 CaO mol. % 0.96 0 1.93 0 Y₂O₃ mol. % 1.95 0 5.83 0 SiO₂mol. % 0 0 0 0.0209 Exemplary Glass Compositions Exemplary Glass 5 6 7 8Composition-mol. % P₂O₅ mol. % 64.98 64.98 64.93 60.02 Al₂O₃ mol. %24.99 19.99 19.98 20.01 B₂O₃ mol. % 0 0 0 0 La₂O₃ mol. % 0 0 0 0 Li₂Omol. % 4.99 7.48 10.00 0 TiO₂ mol. % 5.00 7.51 5.00 10.00 MgO mol. % 0 00 0 Na₂O mol. % 0 0 0 9.97 CeO₂ mol. % 0 0 0 0 CaO mol. % 0.022 0.02160.0426 0 Y₂O₃ mol. % 0 0 0 0 SiO₂ mol. % 0.0205 0.0201 0.0398 0Composition constraints P₂O₅ + B₂O₃ mol. % 67.37 66.58 60.57 64.97 R₂O +RO + SnO₂ + MnO₂ mol. % 9.701 9.949 10.67 2.521 (Li₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 9.701 9.949 10.67 2.521 3 *Al₂O₃ + R₂O + RO − mol. % −0.1054 3.568 1.015 27.51 P₂O₅ Al₂O₃ − R₂O −RO mol. % 7.860 7.585 5.319 27.46 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 5.3715.932 12.77 2.499 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 14.58 17.5513.61 2.521 Composition constraints P₂O₅ + B₂O₃ mol. % 64.98 64.98 64.9360.02 R₂O + RO + SnO₂ + MnO₂ mol. % 5.012 7.506 10.05 9.972 (Li₂O +Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 5.012 7.50610.05 9.972 3 * Al₂O₃ + R₂O + RO − mol. % 15.01 2.493 5.056 9.967 P₂O₅Al₂O₃ − R₂O − RO mol. % 19.98 12.48 9.936 10.03 TiO₂ + La₂O₃ + Y₂O₃ +mol. % 4.998 7.506 4.999 10.00 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol.% 5.012 7.506 10.05 9.972 Measured properties d_(RT) g/cm³ 2.683 2.7272.866 E GPa 72.880 70.743 80.051 μ 0.20900 0.22400 0.20100 E/d_(RT) GPa· cm³/g 27.160 25.950 n_(d) 1.5322 1.5345 v_(d) 68.1 α₂₀₋₃₀₀ × 10⁷ K⁻¹69.140 69.258 66.142 57.000 T_(liq) ° C. 1010 1310 An.P. ° C. 516 507522 T_(soft) ° C. 663 648 665 T_(200 P) ° C. 1187 Log(η_(liq)) P 2.55HCl[DIN12116] mg/cm² 13.34 HCl (5 wt %, 95° C., 24 hrs) mg/cm² 20.170NaOH[ISO695] mg/cm² 121.41 vHF loss mg/cm² 0.29 0.46 Weathering-85°C./85% RH mg/cm² 0.63 Measured properties d_(RT) g/cm³ E GPa 79.84478.603 75.707 81.775 μ 0.20400 0.21000 0.21700 0.21500 E/d_(RT) GPa ·cm³/g n_(d) v_(d) α₂₀₋₃₀₀ × 10⁷ K⁻¹ 64.000 73.000 82.000 69.000 T_(liq)° C. An.P. ° C. T_(soft) ° C. T_(200 P) ° C. Log(η_(liq)) PHCl[DIN12116] mg/cm² HCl (5 wt %, 95° C., 24 hrs) mg/cm² NaOH[ISO695]mg/cm² vHF loss mg/cm² Weathering-85° C./85% RH mg/cm² Predicted andcalculated properties I_(B), mol. % 22.223 28.987 44.751 27.504 P_(E)[for E] GPa 74.65 76.50 77.50 83.14 Predicted and calculated propertiesI_(B), mol. % 15.017 2.5147 5.0371 9.9693 P_(E) [for E] GPa 80.32 77.4976.46 77.09 Exemplary Glass 9 10 11 12 Composition-mol. % P₂O₅ mol. %59.97 59.99 54.99 58.32 Al₂O₃ mol. % 16.99 16.99 14.00 16.01 B₂O₃ mol. %2.00 2.01 2.00 1.99 La₂O₃ mol. % 3.00 0 6.00 2.00 Li₂O mol. % 5.01 5.019.99 2.98 TiO₂ mol. % 5.00 7.99 9.99 6.70 MgO mol. % 3.01 2.99 2.99 4.99Na₂O mol. % 0 0 0 0 CeO₂ mol. % 5.00 5.00 0 7.01 Y₂O₃ mol. % 0 0 0 0SiO₂ mol. % 0.0215 0.0202 0.0418 0 Exemplary Glass 13 14 15 16Composition-mol. % P₂O₅ mol. % 59.18 61.49 57.67 57.56 Al₂O₃ mol. %14.79 17.99 16.31 16.17 B₂O₃ mol. % 7.69 7.50 3.63 2.78 La₂O₃ mol. % 0 04.86 3.97 Li₂O mol. % 3.65 0 7.97 7.14 TiO₂ mol. % 4.95 4.01 0.0838 1.62MgO mol. % 5.93 7.01 2.79 3.44 Na₂O mol. % 0 0 0.50 0.22 CeO₂ mol. %3.79 2.00 1.62 1.32 Y₂O₃ mol. % 0 0 4.56 5.79 SiO₂ mol. % 0.0197 0 0 0Composition constraints P₂O₅ + B₂O₃ mol. % 63.56 63.59 56.99 62.50 R₂O +RO + SnO₂ + MnO₂ mol. % 8.217 8.196 12.98 8.264 (Li₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 8.217 8.196 12.98 8.264 3 *Al₂O₃ + R₂O + RO − mol. % −1.004 −1.051 3.744E−03 −2.397 P₂O5 Al₂O₃ −R₂O − RO mol. % 9.213 9.232 1.022 8.327 TiO₂ + La₂O₃ + Y₂O₃ + mol. %10.77 10.76 15.99 12.64 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 10.2710.26 14.98 10.33 Composition constraints P₂O₅ + B₂O₃ mol. % 68.16 69.6861.80 60.74 R₂O + RO + SnO₂ + MnO₂ mol. % 9.764 7.085 11.35 10.87(Li₂O + Na₂O)/R₂O mol. % 1.000 0 1.000 1.000 R₂O + RO mol. % 9.764 7.08511.35 10.87 3 * Al₂O₃ + R₂O + RO − mol. % −5.321 −0.4993 2.551 1.763P₂O5 Al₂O₃ − R₂O − RO mol. % 5.315 11.09 5.098 5.416 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 6.978 5.056 10.40 12.11 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO +B₂O₃ mol. % 17.60 14.66 15.01 13.66 Measured properties d_(RT) g/cm³2.724 2.654 2.796 2.720 E GPa 75.690 83.200 73.501 69.226 μ 0.214000.20500 0.22300 0.21500 E/d_(RT) GPa · cm³/g 26.100 31.430 26.290 25.450n_(d) 1.553 1.5634 1.5877 1.5582 v_(d) 52.0 46.3 41.7 48.3 T_(liq) ° C.1240 1280 1310 1280 T_(g) ° C. 576 An.P. ° C. 531 556 519 554HCl[DIN12116] mg/cm² 4.78 2.05 9.69 5.82 NaOH[ISO695] mg/cm² 90.05 74.9666.88 77.1 vHF loss mg/cm² 0.29 0.12 0.34 0.39 Weathering-85° C./85% RHmg/cm² 0.41 0.08 0.24 0.35 15-min devit test (0/1) 1 1 1 1 Measuredproperties d_(RT) g/cm³ 2.595 2.560 E GPa 76.397 76.741 μ 0.204000.19900 E/d_(RT) GPa · cm³/g 29.440 29.980 n_(d) 1.5438 1.5341 v_(d)51.8 55.4 T_(liq) ° C. 1265 1250 T_(g) ° C. An.P. ° C. HCl[DIN12116]mg/cm² 3.26 2.29 NaOH[ISO695] mg/cm² 79.38 89.48 vHF loss mg/cm² 0.160.17 Weathering-85° C./85% RH mg/cm² 0.21 0.16 15-min devit test (0/1) 11 Predicted and calculated properties I_(B), mol. % 25.038 16.021 20.10526.724 P_(E) [for E] GPa 77.01 77.57 79.96 77.45 Predicted andcalculated properties I_(B), mol. % 13.839 12.991 39.278 37.734 P_(E)[for E] GPa 75.25 76.39 76.75 77.44 Exemplary Glass 17 18 19 20Composition-mol. % P₂O₅ mol. % 58.90 58.67 59.96 59.97 Al₂O₃ mol. %16.60 16.44 17.01 16.91 B₂O₃ mol. % 3.31 2.58 4.42 3.70 La₂O₃ mol. %3.35 2.72 3.65 2.80 Li₂O mol. % 7.20 6.53 7.96 7.23 TiO₂ mol. % 1.462.67 0.0813 1.42 MgO mol. % 2.86 3.45 1.90 2.44 Na₂O mol. % 0.47 0.210.86 0.65 CeO₂ mol. % 1.12 0.91 1.22 0.93 Y₂O₃ mol. % 4.73 5.83 2.953.96 Exemplary Glass 21 22 23 24 Composition-mol. % P₂O₅ mol. % 59.9059.69 61.42 61.32 Al₂O₃ mol. % 16.82 16.67 17.46 17.33 B₂O₃ mol. % 3.112.39 4.92 4.12 La₂O₃ mol. % 2.19 1.53 2.88 2.05 Li₂O mol. % 6.65 5.997.93 7.14 TiO₂ mol. % 2.47 3.71 0.0638 1.50 MgO mol. % 2.88 3.45 1.331.95 Na₂O mol. % 0.46 0.21 1.11 0.84 CeO₂ mol. % 0.73 0.51 0.96 0.68Y₂O₃ mol. % 4.79 5.86 1.92 3.08 Composition constraints P₂O₅ + B₂O₃ mol.% 62.57 61.53 64.78 63.97 R₂O + RO + SnO₂ + MnO₂ mol. % 10.58 10.2410.78 10.36 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 10.58 10.24 10.78 10.36 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.4220.8313 1.791 1.082 Al₂O₃ − R₂O − RO mol. % 6.110 6.273 6.331 6.635TiO₂ + La₂O₃ + Y₂O₃ + mol. % 10.16 11.73 7.327 8.684 Ce₂O₃ + CeO₂ + ZrO₂R₂O + RO + B₂O₃ mol. % 13.91 12.83 15.23 14.07 Composition constraintsP₂O₅ + B₂O₃ mol. % 63.24 62.23 66.66 65.66 R₂O + RO + SnO₂ + MnO₂ mol. %10.02 9.671 10.42 9.968 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 10.02 9.671 10.42 9.968 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol.% 0.5520 −0.04162 1.341 0.5988 Al₂O₃ − R₂O − RO mol. % 6.863 7.039 7.1247.418 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 9.852 11.38 5.372 6.981 Ce₂O₃ +CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 13.14 12.06 15.37 14.11 Measuredproperties d_(RT) g/cm³ 2.670 2.660 E GPa 69.300 69.100 E/d_(RT) GPa ·cm³/g 25.960 25.980 T_(g) ° C. 536 vHF appearance OK 15-min devit test(0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 2.635 2.700 E GPa 70.90075.400 E/d_(RT) GPa · cm³/g 26.910 27.930 T_(g) ° C. 523 522 vHFappearance OK 15-min devit test (0/1) 1 1 1 1 Predicted and calculatedproperties I_(B), mol. % 32.309 31.772 29.626 27.807 P_(E) [for E] GPa76.69 77.31 75.57 76.11 Predicted and calculated properties I_(B), mol.% 26.803 26.042 23.546 22.145 P_(E) [for E] GPa 76.58 77.19 74.81 75.46Exemplary Glass 25 26 27 28 Composition-mol. % P₂O₅ mol. % 61.22 61.1661.04 59.95 Al₂O₃ mol. % 17.22 17.12 16.97 16.99 B₂O₃ mol. % 3.53 2.942.13 2.00 La₂O₃ mol. % 1.43 0.82 0 6.00 Li₂O mol. % 6.57 6.00 5.27 6.02TiO₂ mol. % 2.55 3.61 5.01 6.00 MgO mol. % 2.42 2.85 3.47 3.00 Na₂O mol.% 0.65 0.45 0.20 0 CeO₂ mol. % 0.48 0.27 0 0.0381 CaO mol. % 0 0 00.0234 Y₂O₃ mol. % 3.93 4.77 5.91 0 Exemplary Glass 29 30 31 32Composition-mol. % P₂O₅ mol. % 59.96 58.42 60.00 58.52 Al₂O₃ mol. %16.99 16.06 17.00 16.13 B₂O₃ mol. % 2.01 2.01 2.00 2.00 La₂O₃ mol. %5.15 6.00 4.52 5.24 Li₂O mol. % 5.72 7.24 5.49 6.90 TiO₂ mol. % 5.727.23 5.51 6.89 MgO mol. % 3.01 2.99 3.00 3.01 Na₂O mol. % 0.0211 0 0.0210.0208 CeO₂ mol. % 1.41 0.0376 2.47 1.27 CaO mol. % 0.0233 0.0231 00.023 Y₂O₃ mol. % 0 0 0 0 Composition constraints P₂O₅ + B₂O₃ mol. %64.91 64.18 63.17 61.96 R₂O + RO + SnO₂ + MnO₂ mol. % 9.666 9.318 8.9359.036 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. %9.666 9.318 8.935 9.036 3 * Al₂O₃ + R₂O + RO − mol. % 0.06508 −0.4793−1.178 0.03884 P₂O₅ Al₂O₃ − R₂O − RO mol. % 7.591 7.830 8.039 7.954TiO₂ + La₂O₃ + Y₂O₃ + mol. % 8.171 9.349 10.92 12.01 Ce₂O₃ + CeO₂ + ZrO₂R₂O + RO + B₂O₃ mol. % 13.20 12.26 11.07 11.03 Composition constraintsP₂O₅ + B₂O₃ mol. % 62.40 60.44 62.77 60.90 R₂O + RO + SnO₂ + MnO₂ mol. %8.839 10.25 8.617 10.02 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 8.839 10.25 8.617 10.02 3 * Al₂O₃ + R₂O + RO − mol. %−0.2246 4.816E−03 −0.4980 −0.1643 P₂O₅ Al₂O₃ − R₂O − RO mol. % 8.2665.817 8.595 6.219 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 11.65 13.25 11.40 12.84Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 10.86 12.26 10.64 12.03Measured properties d_(RT) g/cm³ 2.590 2.550 E GPa 72.400 72.000E/d_(RT) GPa · cm³/g 27.950 28.240 α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 15-min devit test(0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 2.710 E GPa 72.900E/d_(RT) GPa · cm³/g 26.900 α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 66.000 15-min devit test(0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol. % 21.09120.080 18.667 20.114 P_(E) [for E] GPa 75.93 76.41 77.03 78.34 Predictedand calculated properties I_(B), mol. % 21.426 20.100 22.490 21.316P_(E) [for E] GPa 77.97 78.84 77.68 78.49 Exemplary Glass 33 34 35 36Composition-mol. % P₂O₅ mol. % 57.34 60.00 58.53 57.48 Al₂O₃ mol. %15.41 17.00 16.13 15.50 B₂O₃ mol. % 2.01 1.99 1.99 2.00 La₂O₃ mol. %6.00 3.88 4.65 5.25 Li₂O mol. % 8.11 5.29 6.71 7.74 TiO₂ mol. % 8.095.29 6.69 7.74 MgO mol. % 2.99 2.99 3.00 3.01 Na₂O mol. % 0 0.02090.0207 0.0206 CeO₂ mol. % 0.0372 3.54 2.26 1.25 CaO mol. % 0.0229 00.0229 0.0228 Exemplary Glass 37 38 39 40 Composition-mol. % P₂O₅ mol. %56.30 58.42 57.31 56.29 Al₂O₃ mol. % 14.80 16.06 15.40 14.78 B₂O₃ mol. %2.01 2.00 2.01 2.00 La₂O₃ mol. % 6.00 3.94 4.59 5.21 Li₂O mol. % 8.936.55 7.65 8.67 TiO₂ mol. % 8.92 6.56 7.65 8.68 MgO mol. % 2.99 3.01 3.003.01 Na₂O mol. % 0 0.0206 0.0205 0.0204 CeO₂ mol. % 0.0369 3.43 2.351.31 CaO mol. % 0.0227 0 0.0227 0.0225 Composition constraints P₂O₅ +B₂O₃ mol. % 59.36 63.11 61.21 59.85 R₂O + RO + SnO₂ + MnO₂ mol. % 11.128.455 9.861 10.86 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O +RO mol. % 11.12 8.455 9.861 10.86 3 * Al₂O₃ + R₂O + RO − mol. % 0.02417−0.7045 −0.3870 −0.1954 P₂O₅ Al₂O₃ − R₂O − RO mol. % 4.294 8.851 6.4564.735 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 14.11 11.13 12.61 13.70 Ce₂O₃ +CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 13.13 10.48 11.88 12.87 Compositionconstraints P₂O₅ + B₂O₃ mol. % 58.32 61.48 60.02 58.67 R₂O + RO + SnO₂ +MnO₂ mol. % 11.94 9.748 10.82 11.80 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 11.94 9.748 10.82 11.80 3 * Al₂O₃ + R₂O + RO− mol. % 0.02909 −0.6631 −0.4212 −0.2223 P₂O₅ Al₂O₃ − R₂O − RO mol. %2.856 6.596 4.766 3.083 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 14.94 12.43 13.5714.65 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 13.95 11.78 12.85 13.81Measured properties d_(RT) g/cm³ 2.670 E GPa 71.700 E/d_(RT) GPa · cm³/g26.850 α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 63.600 15-min devit test (0/1) 1 1 1 1 Measuredproperties d_(RT) g/cm³ 2.710 E GPa 72.600 E/d_(RT) GPa · cm³/g 26.790α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 69.700 15-min devit test (0/1) 1 1 1 1 Predicted andcalculated properties I_(B), mol. % 20.112 23.570 22.296 21.258 P_(E)[for E] GPa 79.20 77.40 78.22 78.83 Predicted and calculated propertiesI_(B), mol. % 20.118 23.471 22.380 21.337 P_(E) [for E] GPa 79.54 77.9578.60 79.20 Exemplary Glass 41 42 43 44 Composition-mol. % P₂O₅ mol. %56.90 59.48 54.74 56.72 Al₂O₃ mol. % 16.98 16.70 16.99 16.73 B₂O₃ mol. %5.05 1.99 7.21 4.80 La₂O₃ mol. % 3.00 2.71 3.00 2.74 Li₂O mol. % 3.484.43 2.39 3.05 TiO₂ mol. % 5.00 5.50 4.99 5.45 MgO mol. % 4.53 3.57 5.604.93 Na₂O mol. % 0.0409 0.0415 0.0607 0.0409 CeO₂ mol. % 5.00 5.58 5.005.52 CaO mol. % 0.0226 0 0.0224 0.0226 Exemplary Glass 45 46 47 48Composition-mol. % P₂O₅ mol. % 59.12 54.63 56.39 58.76 Al₂O₃ mol. %16.48 16.72 16.52 16.28 B₂O₃ mol. % 2.01 6.87 4.79 2.00 La₂O₃ mol. %2.49 2.74 2.54 2.28 Li₂O mol. % 3.99 2.05 2.66 3.55 TiO₂ mol. % 5.855.44 5.79 6.22 MgO mol. % 4.01 5.96 5.33 4.44 Na₂O mol. % 0.0413 0.06060.0408 0.0412 CeO₂ mol. % 6.01 5.51 5.93 6.44 CaO mol. % 0 0.0223 0.02250 Composition constraints P₂O₅ + B₂O₃ mol. % 63.53 63.23 63.54 63.26R₂O + RO + SnO₂ + MnO₂ mol. % 8.283 8.269 8.283 8.274 (Li₂O + Na₂O)/R₂Omol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 8.283 8.269 8.283 8.2743 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.178 −1.366 4.402 1.547 Al₂O₃ − R₂O− RO mol. % 9.133 8.914 9.138 8.926 TiO₂ + LaO₃ + Y ₂O₃ + mol. % 10.7711.31 10.76 11.26 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 13.46 10.3215.67 13.21 Composition constraints P₂O₅ + B₂O₃ mol. % 63.02 63.24 63.0462.78 R₂O + RO + SnO₂ + MnO₂ mol. % 8.282 8.327 8.298 8.294 (Li₂O +Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 8.282 8.3278.298 8.294 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % −1.688 3.733 1.269 −1.971Al₂O₃ − R₂O − RO mol. % 8.712 8.866 8.729 8.522 TiO₂ + LaO₃ + Y ₂O₃ +mol. % 11.70 11.24 11.63 12.11 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol.% 10.35 15.39 13.23 10.36 Measured properties E GPa 72.390 15-min devittest (0/1) 1 1 1 1 Measured properties E GPa 77.460 15-min devit test(0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol. % 31.12925.537 35.464 31.091 P_(E) [for E] GPa 78.58 77.13 79.69 78.57 Predictedand calculated properties I_(B), mol. % 25.881 35.221 31.402 26.253P_(E) [for E] GPa 77.21 79.64 78.65 77.31 Exemplary Glass 49 50 51 52Composition-mol. % P₂O₅ mol. % 53.97 55.76 59.49 58.92 Al₂O₃ mol. %16.50 16.28 17.49 18.06 B₂O₃ mol. % 7.14 5.00 2.00 1.99 La₂O₃ mol. %2.51 2.30 3.00 3.00 Li₂O mol. % 1.46 2.10 5.00 4.99 TiO₂ mol. % 5.826.18 5.00 5.00 MgO mol. % 6.55 5.89 3.00 3.00 Na₂O mol. % 0.0603 0.06080.0208 0.0415 ZrO₂ mol. % 0 0 0 0 CeO₂ mol. % 5.97 6.40 5.00 5.00 CaOmol. % 0.0222 0.0224 0 0 Exemplary Glass 53 54 55 56 Composition-mol. %P₂O₅ mol. % 59.01 58.49 58.52 58.04 Al₂O₃ mol. % 17.61 18.48 18.12 18.90B₂O₃ mol. % 2.04 1.99 2.04 2.01 La₂O₃ mol. % 3.05 3.00 3.04 3.00 Li₂Omol. % 5.09 4.98 5.09 5.02 TiO₂ mol. % 5.07 5.00 5.07 4.99 MgO mol. %3.05 2.99 3.04 2.99 Na₂O mol. % 0.0206 0.0414 0.0206 0.0414 ZrO₂ mol. %1.52 0 1.41 0 CeO₂ mol. % 3.56 5.00 3.66 5.00 CaO mol. % 0 0.0229 00.0229 Composition constraints P₂O₅ + B₂O₃ mol. % 62.99 62.76 63.0662.47 R₂O + RO + SnO₂ + MnO₂ mol. % 8.345 8.347 8.229 8.234 (Li₂O +Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 8.345 8.3478.229 8.234 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 3.732 1.213 1.040 3.385Al₂O₃ − R₂O − RO mol. % 8.660 8.475 9.712 10.29 TiO₂ + La₂O₃ + Y₂O₃ +mol. % 11.66 12.07 10.77 10.77 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol.% 15.71 13.51 10.28 10.28 Composition constraints P₂O₅ + B₂O₃ mol. %62.15 62.03 61.68 61.58 R₂O + RO + SnO₂ + MnO₂ mol. % 8.305 8.247 8.2998.277 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. %8.305 8.247 8.299 8.277 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.002 5.1224.068 6.910 Al₂O₃ − R₂O − RO mol. % 9.619 10.71 10.16 11.11 TiO₂ +La₂O₃ + Y₂O₃ + mol. % 11.62 10.76 11.56 10.75 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 10.38 10.29 10.37 10.33 Measured properties E GPa88.920 15-min devit test (0/1) 1 1 1 1 Measured properties E GPa 93.03086.740 90.590 15-min devit test (0/1) 1 1 1 1 Predicted and calculatedproperties I_(B), mol. % 36.166 32.226 27.020 29.296 P_(E) [for E] GPa79.89 78.87 77.63 78.35 Predicted and calculated properties I_(B), mol.% 23.797 30.986 26.114 32.702 P_(E) [for E] GPa 78.97 78.88 79.53 79.42Exemplary Glass 57 58 59 60 Composition-mol. % P₂O₅ mol. % 58.11 58.7656.47 55.69 Al₂O₃ mol. % 18.52 16.09 16.12 15.36 B₂O₃ mol. % 2.03 2.922.87 3.63 WO₃ mol. % 0 0 0 0 La₂O₃ mol. % 3.04 0 0.88 0.79 Nb₂O₅ mol. %0 0 0 0 Li₂O mol. % 5.08 5.00 5.60 5.52 TiO₂ mol. % 5.06 9.82 8.58 10.21MgO mol. % 3.04 3.29 4.45 4.59 Na₂O mol. % 0.0412 0.0386 0.0389 0.0383ZrO₂ mol. % 1.42 0 0 0 CeO₂ mol. % 3.65 4.08 5.00 4.16 CaO mol. % 0 0 00 Y₂O₃ mol. % 0 0 0 0 SiO₂ mol. % 0 0 0 0 TaO₅ mol. % 0 0 0 0 ExemplaryGlass 61 62 63 64 Composition-mol. % P₂O₅ mol. % 53.91 53.28 52.09 0Al₂O₃ mol. % 15.48 14.76 14.00 0 B₂O₃ mol. % 3.52 4.23 4.99 21.48 WO₃mol. % 0 0 0 20.98 La₂O₃ mol. % 1.52 1.40 1.46 17.09 Nb₂O₅ mol. % 0 0 017.19 Li₂O mol. % 6.00 5.92 5.99 0.82 TiO₂ mol. % 9.01 10.59 12.05 12.29MgO mol. % 5.52 5.62 5.94 0.70 Na₂O mol. % 0.0386 0.038 0.0375 0 ZrO₂mol. % 0 0 0 8.00 CeO₂ mol. % 5.00 4.16 3.46 0 CaO mol. % 0 0 0 0.60Y₂O₃ mol. % 0 0 0 0.80 SiO₂ mol. % 0 0 0 0.0312 TaO₅ mol. % 0 0 0 0.017Composition constraints P₂O₅ + B₂O₃ mol. % 61.26 62.97 60.86 60.58 R₂O +RO + SnO₂ + MnO₂ mol. % 8.309 8.506 10.35 10.37 (Li₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 8.309 8.506 10.35 10.37 3 *Al₂O₃ + R₂O + RO − P₂O₅ mol. % 5.722 −2.215 2.022 0.5648 Al₂O₃ − R₂O −RO mol. % 10.56 7.916 6.182 5.323 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 11.5612.11 12.26 13.36 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 10.38 11.4913.29 14.08 Composition constraints P₂O₅ + B₂O₃ mol. % 58.91 58.74 58.0821.48 R₂O + RO + SnO₂ + MnO₂ mol. % 11.85 11.82 12.18 2.114 (Li₂O +Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.85 11.8212.18 2.114 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 4.182 2.625 1.902 2.114Al₂O₃ − R₂O − RO mol. % 4.021 3.260 2.066 −2.114 TiO₂ + La₂O₃ + Y₂O₃ +mol. % 13.36 14.37 15.50 38.18 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol.% 15.46 16.14 17.26 23.60 Measured properties d_(RT) g/cm³ 2.653 2.644 EGPa 91.090 E/d_(RT) GPa · cm³/g T_(g) ° C. T_(x) T_(x)-T_(g) ° C. 15-mindevit test (0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 2.665 2.6582.662 E GPa 76.200 79.600 79.600 123.00 E/d_(RT) GPa · cm³/g 28.59029.950 29.900 T_(g) ° C. 545 559 T_(x) 787 765 T_(x)-T_(g) ° C. 242 20615-min devit test (0/1) 1 1 1 Predicted and calculated properties I_(B),mol. % 27.710 12.999 22.469 19.061 P_(E) [for E] GPa 80.04 78.28 79.0479.54 Predicted and calculated properties I_(B), mol. % 27.172 23.48121.601 77.269 P_(E) [for E] GPa 80.11 80.54 81.17 111.2 Exemplary Glass65 66 67 68 Composition-mol. % B₂O₃ mol. % 21.77 21.78 21.98 22.02 WO₃mol. % 20.56 20.55 20.25 20.19 La₂O₃ mol. % 17.74 16.89 18.23 17.50Nb₂O₂ mol. % 16.77 16.75 16.45 16.39 Li₂O mol. % 0.81 0.81 0.81 0.81TiO₂ mol. % 12.72 12.73 13.03 13.09 MgO mol. % 0.70 0.69 0.70 0.69 ZrO₂mol. % 7.71 7.71 7.51 7.46 CaO mol. % 0.60 0.60 0.60 0.60 Y₂O₃ mol. %0.57 1.44 0.41 1.20 SiO₂ mol. % 0.0311 0.031 0.0311 0.031 TaO₅ mol. %0.0169 0.0169 0.0169 0.0168 Exemplary Glass 69 70 71 72 Composition-mol.% B₂O₃ mol. % 21.99 22.20 22.23 22.24 WO₃ mol. % 20.23 19.92 19.89 19.89La₂O₃ mol. % 16.74 18.72 17.95 17.35 Nb₂O₂ mol. % 16.43 16.13 16.0916.09 Li₂O mol. % 0.81 0.81 0.81 0.81 TiO₂ mol. % 13.07 13.36 13.4013.40 MgO mol. % 0.69 0.69 0.69 0.69 ZrO₂ mol. % 7.49 7.29 7.27 7.26 CaOmol. % 0.60 0.60 0.60 0.59 Y₂O₃ mol. % 1.91 0.23 1.04 1.65 SiO₂ mol. %0.0309 0.0311 0.0309 0.0308 TaO₅ mol. % 0.0168 0.0169 0.0168 0.0168Composition constraints P₂O₅ + B₂O₃ mol. % 21.77 21.78 21.98 22.02 R₂O +RO + SnO₂ + MnO₂ mol. % 2.111 2.101 2.108 2.099 (Li₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 2.111 2.101 2.108 2.099 3 *Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.111 2.101 2.108 2.099 Al₂O₃ − R₂O − ROmol. % −2.111 −2.101 −2.108 −2.099 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 38.7438.77 39.17 39.24 Ce₂O₃ + CeO₂ + mol. % ZrO₂ R₂O + RO + B₂O₃ mol. %23.88 23.88 24.09 24.12 Composition constraints P₂O₅ + B₂O₃ mol. % 21.9922.20 22.23 22.24 R₂O + RO + SnO₂ + MnO₂ mol. % 2.091 2.106 2.096 2.089(Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 2.0912.106 2.096 2.089 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.091 2.106 2.0962.089 Al₂O₃ − R₂O − RO mol. % −2.091 −2.106 −2.096 −2.089 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 39.21 39.60 39.65 39.66 Ce₂O₃ + CeO₂ + mol. % ZrO₂ R₂O +RO + B₂O₃ mol. % 24.08 24.30 24.32 24.32 Measured properties vHF lossmg/cm² 0.1 vHF appearance shiny 15-min devit test (0/1) 1 1 1 1 Measuredproperties vHF loss mg/cm² vHF appearance 15-min devit test (0/1) 1 1 11 Predicted and calculated properties I_(B), mol. % 78.821 78.876 79.98480.192 P_(E) [for E] GPa 111.1 111.1 111.1 111.0 Predicted andcalculated properties I_(B), mol. % 80.059 81.167 81.299 81.322 P_(E)[for E] GPa 111.0 111.0 111.0 110.9 Exemplary Glass 73 74 75 76Composition-mol. % P₂O₅ mol. % 0 0 0 0 Al₂O₃ mol. % 0 0 0 0 B₂O₃ mol. %22.21 22.48 22.49 22.49 WO₃ mol. % 19.91 19.49 19.50 19.49 La₂O₃ mol. %16.59 19.39 18.50 17.86 Nb₂O₅ mol. % 16.12 15.70 15.69 15.69 Li₂O mol. %0.80 0.81 0.81 0.80 TiO₂ mol. % 13.38 13.79 13.79 13.79 MgO mol. % 0.690.69 0.69 0.69 Na₂O mol. % 0 0 0 0 ZrO₂ mol. % 7.28 7.00 7.00 7.01 CaOmol. % 0.59 0.60 0.60 0.59 Y₂O₃ mol. % 2.38 0 0.90 1.54 SiO₂ mol. %0.0307 0.031 0.0309 0.0308 TaO₅ mol. % 0.0167 0.0127 0.0126 0.0167Exemplary Glass 77 78 79 80 Composition-mol. % P₂O₅ mol. % 0 0 63.5763.49 Al₂O₃ mol. % 0 0 17.49 17.49 B₂O₃ mol. % 22.49 22.50 7.19 6.63 WO₃mol. % 19.50 19.50 0 0 La₂O₃ mol. % 17.23 16.40 0 0 Nb₂O₅ mol. % 15.7015.70 0 0 Li₂O mol. % 0.80 0.80 7.20 6.20 TiO₂ mol. % 13.79 13.80 0 0MgO mol. % 0.69 0.68 3.99 4.01 Na₂O mol. % 0 0 0.019 1.07 ZrO₂ mol. %7.00 7.00 0.50 1.07 CaO mol. % 0.59 0.59 0.021 0.0211 Y₂O₃ mol. % 2.173.00 0 0 SiO₂ mol. % 0.0307 0.0305 0.0196 0.0196 TaO₅ mol. % 0.01670.0166 0 0 Composition constraints P₂O₅ + B₂O₃ mol. % 22.21 22.48 22.4922.49 R₂O + RO + SnO₂ + MnO₂ mol. % 2.082 2.102 2.093 2.085 (Li₂O +Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 2.082 2.1022.093 2.085 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.082 2.102 2.093 2.085Al₂O₃ − R₂O − RO mol. % −2.082 −2.102 −2.093 −2.085 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 39.63 40.18 40.19 40.19 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO +B₂O₃ mol. % 24.29 24.59 24.58 24.57 Composition constraints P₂O₅ + B₂O₃mol. % 22.49 22.50 70.76 70.12 R₂O + RO + SnO₂ + MnO₂ mol. % 2.078 2.06911.23 11.30 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 2.078 2.069 11.23 11.30 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 2.0782.069 0.1359 0.2797 Al₂O₃ − R₂O − RO mol. % −2.078 −2.069 6.263 6.190TiO₂ + La₂O₃ + Y₂O₃ + mol. % 40.19 40.19 0.4958 1.073 Ce₂O₃ + CeO₂ +ZrO₂ R₂O + RO + B₂O₃ mol. % 24.57 24.57 18.42 17.93 Measured properties15-min devit test (0/1) 1 1 1 1 E GPa 123.90 α²⁰⁻³⁰⁰ × 10⁷ K¹ Measuredproperties 15-min devit test (0/1) 1 1 1 1 E GPa 123.80 87.800 α²⁰⁻³⁰⁰ ×10⁷ K¹ 71.800 Predicted and calculated properties I_(B), mol. % 81.22382.768 82.763 82.770 P_(E) [for E] GPa 110.9 111.0 110.9 110.9 Predictedand calculated properties I_(B), mol. % 82.761 82.762 7.3325 6.8716P_(E) [for E] GPa 110.8 110.8 73.71 73.68 Exemplary Glass 81 82 83 84Composition-mol. % P₂O₅ mol. % 63.56 63.48 63.49 63.57 Al₂O₃ mol. %17.49 17.49 17.48 17.50 B₂O₃ mol. % 6.63 6.20 6.14 6.20 Li₂O mol. % 7.205.43 6.28 7.20 TiO₂ mol. % 0.57 0 0.53 0.99 MgO mol. % 4.00 4.00 4.014.00 Na₂O mol. % 0.019 1.86 0.99 0.019 ZrO₂ mol. % 0.50 1.50 1.04 0.50CaO mol. % 0.021 0.0211 0.0211 0.021 SiO₂ mol. % 0.0196 0.0197 0.01970.0196 Exemplary Glass 85 86 87 88 Composition-mol. % P₂O₅ mol. % 63.4363.48 63.53 63.56 Al₂O₃ mol. % 17.50 17.49 17.50 17.49 B₂O₃ mol. % 5.775.74 5.74 5.78 Li₂O mol. % 4.70 5.55 6.25 7.20 TiO₂ mol. % 0 0.52 0.931.41 MgO mol. % 4.01 4.00 3.99 4.00 Na₂O mol. % 2.63 1.74 0.99 0.019ZrO₂ mol. % 1.92 1.44 1.04 0.50 CaO mol. % 0.0212 0.0211 0.0211 0.021SiO₂ mol. % 0.0198 0.0197 0.0197 0.0196 Composition constraints P₂O₅ +B₂O₃ mol. % 70.19 69.68 69.63 69.76 R₂O + RO + SnO₂ + MnO₂ mol. % 11.2311.31 11.30 11.24 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O +RO mol. % 11.23 11.31 11.30 11.24 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %0.1345 0.3085 0.2561 0.1594 Al₂O₃ − R₂O − RO mol. % 6.254 6.185 6.1766.257 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 1.070 1.500 1.567 1.483 Ce₂O₃ +CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 17.87 17.51 17.44 17.44 Compositionconstraints P₂O₅ + B₂O₃ mol. % 69.20 69.22 69.27 69.34 R₂O + RO + SnO₂ +MnO₂ mol. % 11.36 11.31 11.25 11.24 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 11.36 11.31 11.25 11.24 3 * Al₂O₃ + R₂O + RO− P₂O₅ mol. % 0.4225 0.3044 0.2042 0.1414 Al₂O₃ − R₂O − RO mol. % 6.1376.180 6.251 6.247 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 1.921 1.962 1.967 1.910Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 17.13 17.05 16.98 17.02Measured properties 15-min devit test (0/1) 1 1 1 1 NaOH[ISO695] mg/cm²Measured properties 15-min devit test (0/1) 1 1 1 1 NaOH[ISO695] mg/cm²90 90 Predicted and calculated properties I_(B), mol. % 6.7587 6.51586.3585 6.3553 P_(E) [for E] GPa 73.93 73.63 73.88 74.09 Predicted andcalculated properties I_(B), mol. % 6.1895 6.0352 5.9613 5.9065 P_(E)[for E] GPa 73.60 73.84 74.02 74.25 Exemplary Glass 89 90 91 92Composition-mol. % P₂O₅ mol. % 63.35 63.43 63.47 63.53 Al₂O₃ mol. %17.48 17.50 17.50 17.50 B₂O₃ mol. % 5.20 5.20 5.20 5.20 Li₂O mol. % 3.724.70 5.44 6.17 TiO₂ mol. % 0 0.57 0.99 1.42 MgO mol. % 4.00 3.99 4.003.99 Na₂O mol. % 3.70 2.65 1.86 1.07 ZrO₂ mol. % 2.50 1.93 1.50 1.08 CaOmol. % 0.0213 0.0212 0.0212 0.0211 K₂O mol. % 0 0 0 0 SiO₂ mol. % 0.01990.0198 0.0197 0.0197 Exemplary Glass 93 94 95 96 Composition-mol. % P₂O₅mol. % 63.56 65.31 65.46 65.27 Al₂O₃ mol. % 17.48 16.98 16.97 16.97 B₂O₃mol. % 5.21 7.81 7.79 7.79 Li₂O mol. % 7.21 7.78 5.63 5.67 TiO₂ mol. %2.00 0 0 0 MgO mol. % 4.00 2.06 2.93 3.08 Na₂O mol. % 0 0.0191 1.17 0.62ZrO₂ mol. % 0.50 0 0 0 CaO mol. % 0.021 0.0212 0.0213 0.0213 K₂O mol. %0 0 0 0.57 SiO₂ mol. % 0.0196 0.0198 0.0199 0.0199 Compositionconstraints P₂O₅ + B₂O₃ mol. % 68.55 68.63 68.67 68.72 R₂O + RO + SnO₂ +MnO₂ mol. % 11.44 11.36 11.32 11.25 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 11.44 11.36 11.32 11.25 K₂O + Rb₂O + CS₂Omol. % 0 0 0 0 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 0.5446 0.4109 0.33230.2250 Al₂O₃ − R₂O − RO mol. % 6.041 6.139 6.178 6.247 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 2.502 2.498 2.496 2.505 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO +B₂O₃ mol. % 16.64 16.55 16.51 16.45 Composition constraints P₂O₅ + B₂O₃mol. % 68.77 73.12 73.26 73.06 R₂O + RO + SnO₂ + MnO₂ mol. % 11.23 9.8849.752 9.950 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 0.9169 R₂O + ROmol. % 11.23 9.884 9.752 9.950 K₂O + Rb₂O + CS₂O mol. % 0 0 0 0.5697 3 *Al₂O₃ + R₂O + RO − P₂O₅ mol. % 0.1210 −4.491 −4.792 −4.407 Al₂O₃ − R₂O −RO mol. % 6.257 7.095 7.220 7.019 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 2.500 0 00 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 16.43 17.69 17.55 17.74Measured properties d_(RT) g/cm³ E GPa 88.300 E/d_(RT) GPa · cm³/gα²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 74.100 vHF loss mg/cm² 0.1 0.1 vHF appearance clear.clear. shiny shiny 15-min devit test (0/1) 1 1 1 1 Measured propertiesd_(RT) g/cm³ 2.535 E GPa 88.900 88.400 E/d_(RT) GPa · cm³/g 34.870α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 70.200 vHF loss mg/cm² vHF appearance 15-min devittest (0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol. %5.7073 5.6087 5.5308 5.4491 P_(E) [for E] GPa 73.55 73.81 74.01 74.21Predicted and calculated properties I_(B), mol. % 5.3181 3.8075 2.99843.3771 P_(E) [for E] GPa 74.47 76.28 76.06 75.57 Exemplary Glass 97 9899 100 Composition mol. % P₂O₅ mol. % 65.56 65.42 65.25 65.72 Al₂O₃ mol.% 16.97 16.98 16.96 16.98 B₂O₃ mol. % 7.81 7.79 7.81 7.81 Li₂O mol. %4.05 3.81 4.05 2.41 MgO mol. % 3.56 3.80 3.86 4.21 Na₂O mol. % 2.01 1.621.04 2.87 CaO mol. % 0.0213 0.0214 0.0214 0 K₂O mol. % 0 0.53 0.99 0SiO₂ mol. % 0.0199 0.0199 0.0199 0 Exemplary Glass 101 102 103 104Composition mol. % P₂O₅ mol. % 65.56 65.42 65.89 65.69 Al₂O₃ mol. %16.98 16.97 16.98 16.97 B₂O₃ mol. % 7.81 7.81 7.80 7.81 Li₂O mol. % 2.252.29 0.20 0.24 MgO mol. % 4.45 4.54 5.10 5.25 Na₂O mol. % 2.43 2.04 4.043.45 CaO mol. % 0 0 0 0 K₂O mol. % 0.52 0.93 0 0.58 SiO₂ mol. % 0 0 0 0Composition constraints P₂O₅ + B₂O₃ mol. % 73.37 73.21 73.05 73.53 R₂O +RO + SnO₂ + MnO₂ mol. % 9.639 9.791 9.963 9.492 (Li₂O + Na₂O)/R₂O mol. %1.000 0.9105 0.8370 1.000 R₂O + RO mol. % 9.639 9.791 9.963 9.492 K₂O +Rb₂O + Cs₂O mol. % 0 0.5341 0.9912 0 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %−4.999 −4.699 −4.391 −5.281 Al₂O₃ − R₂O − RO mol. % 7.336 7.185 7.0027.490 R₂O + RO + B₂O₃ mol. % 17.44 17.59 17.77 17.30 Compositionconstraints P₂O₅ + B₂O₃ mol. % 73.37 73.23 73.68 73.51 R₂O + RO + SnO₂ +MnO₂ mol. % 9.650 9.798 9.338 9.520 (Li₂O + Na₂O)/R₂O mol. % 0.89940.8229 1.000 0.8648 R₂O + RO mol. % 9.650 9.798 9.338 9.520 K₂O + Rb₂O +Cs₂O mol. % 0.5236 0.9320 0 0.5774 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %−4.985 −4.707 −5.619 −5.248 Al₂O₃ − R₂O − RO mol. % 7.326 7.174 7.6397.455 R₂O + RO + B₂O₃ mol. % 17.46 17.61 17.13 17.33 Measured propertiesd_(RT) g/cm³ 2.549 E GPa 89.700 E/d_(RT) GPa · cm³/g 35.190 15-min devittest (0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 2.556 E GPa 88.000E/d_(RT) GPa · cm³/g 34.430 15-min devit test (0/1) 1 1 1 1 Predictedand calculated properties I_(B), mol. % 2.7833 3.0922 3.3995 2.5354P_(E) [for E] GPa 75.90 75.43 75.09 75.78 Predicted and calculatedproperties I_(B), mol. % 2.8391 3.1031 2.1917 2.5753 P_(E) [for E] GPa75.35 74.99 75.58 75.11 Exemplary Glass 105 106 107 108 Composition-mol.% P₂O₅ mol. % 62.94 63.12 62.93 62.74 Al₂O₃ mol. % 17.45 17.63 17.7517.85 B₂O₃ mol. % 5.22 5.72 6.10 6.48 Li₂O mol. % 3.98 2.65 1.85 1.05TiO₂ mol. % 0 0 0.0151 0.0151 MgO mol. % 4.14 3.99 4.00 4.01 Na₂O mol. %3.75 4.06 4.35 4.63 ZrO₂ mol. % 2.48 2.78 3.00 3.21 CaO mol. % 0.02120.0214 0 0 SiO₂ mol. % 0.0198 0.02 0.02 0.0201 Exemplary Glass 109 110111 112 Composition-mol. % P₂O₅ mol. % 62.49 66.20 66.21 65.84 Al₂O₃mol. % 18.00 17.00 17.00 17.29 B₂O₃ mol. % 7.00 7.80 7.80 7.85 Li₂O mol.% 0 0 0 0 TiO₂ mol. % 0.0151 0 0 0 MgO mol. % 3.99 4.99 6.15 3.57 Na₂Omol. % 5.00 4.01 2.83 4.29 ZrO₂ mol. % 3.51 0 0 1.15 CaO mol. % 0 0 0 0SiO₂ mol. % 0 0 0 0 Composition constraints P₂O₅ + B₂O₃ mol. % 68.1668.84 69.03 69.22 R₂O + RO + SnO₂ + MnO₂ mol. % 11.89 10.72 10.19 9.686(Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.8910.72 10.19 9.686 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.308 0.5017 0.50790.5002 Al₂O₃ − R₂O − RO mol. % 5.569 6.911 7.554 8.167 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 2.483 2.784 3.011 3.224 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO +B₂O₃ mol. % 17.10 16.44 16.29 16.16 Composition constraints P₂O₅ + B₂O₃mol. % 69.49 74.00 74.01 73.70 R₂O + RO + SnO₂ + MnO₂ mol. % 8.988 9.0028.984 7.867 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 8.988 9.002 8.984 7.867 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 0.4885−6.188 −6.215 −6.117 Al₂O₃ − R₂O − RO mol. % 9.009 7.999 8.020 9.420TiO₂ + La₂O₃ + Y₂O₃ + mol. % 3.520 0 0 1.149 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 15.99 16.80 16.79 15.72 Measured properties 15-mindevit test (0/1) 1 1 1 1 Measured properties 15-min devit test (0/1) 1 11 1 Predicted and calculated properties I_(B), mol. % 6.5449 6.21326.6130 6.9886 P_(E) [for E] GPa 73.69 73.83 74.04 74.24 Predicted andcalculated properties I_(B), mol. % 7.4997 1.6182 1.6038 1.7250 P_(E)[for E] GPa 74.53 75.99 76.46 76.86 Exemplary Glass 113 114 115 116Composition-mol. % P₂O₅ mol. % 66.20 65.88 65.61 66.20 Al₂O₃ mol. %17.00 17.26 17.50 17.00 B₂O₃ mol. % 7.81 7.85 7.90 7.80 MgO mol. % 7.014.77 2.50 7.87 Na₂O mol. % 1.99 3.18 4.50 1.13 ZrO₂ mol. % 0 1.06 1.99 0Exemplary Glass 117 118 119 120 Composition-mol. % P₂O₅ mol. % 65.8865.62 65.35 65.87 Al₂O₃ mol. % 17.26 17.46 17.71 17.29 B₂O₃ mol. % 7.867.89 7.94 7.85 MgO mol. % 5.58 3.76 1.44 6.45 Na₂O mol. % 2.37 3.40 4.721.41 ZrO₂ mol. % 1.05 1.87 2.84 1.13 Composition constraints P₂O₅ + B₂O₃mol. % 74.00 73.73 73.51 74.00 R₂O + RO + SnO₂ + MnO₂ mol. % 9.000 7.9566.993 9.000 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 9.000 7.956 6.993 9.000 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % −6.204−6.148 −6.112 −6.207 Al₂O₃ − R₂O − RO mol. % 7.998 9.301 10.51 8.000TiO₂ + La₂O₃ + Y₂O₃ + mol. % 0 1.057 1.992 0 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 16.81 15.81 14.89 16.80 Composition constraints P₂O₅ +B₂O₃ mol. % 73.74 73.51 73.29 73.72 R₂O + RO + SnO₂ + MnO₂ mol. % 7.9557.160 6.156 7.861 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O +RO mol. % 7.955 7.160 6.156 7.861 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %−6.160 −6.083 −6.053 −6.148 Al₂O₃ − R₂O − RO mol. % 9.301 10.30 11.569.426 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 1.046 1.867 2.843 1.134 Ce₂O₃ +CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 15.81 15.05 14.09 15.71 Measuredproperties 15-min devit test (0/1) 1 1 1 1 Measured properties 15-mindevit test (0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol.% 1.5959 1.6940 1.8025 1.5975 P_(E) [for E] GPa 76.78 77.23 77.54 77.12Predicted and calculated properties I_(B), mol. % 1.6889 1.7834 1.88621.7208 P_(E) [for E] GPa 77.55 77.83 78.18 77.99 Exemplary Glass 121 122123 124 Composition-mol. % P₂O₅ mol. % 65.61 65.36 64.99 65.48 Al₂O₃mol. % 17.50 17.71 17.99 16.99 B₂O₃ mol. % 7.90 7.94 7.99 7.80 Li₂O mol.% 0 0 0 5.50 TiO₂ mol. % 0 0 0.0156 0 MgO mol. % 4.55 2.63 0 4.19 Na₂Omol. % 2.47 3.54 5.01 0 ZrO₂ mol. % 1.98 2.83 4.00 0 CaO mol. % 0 0 00.0212 SiO₂ mol. % 0 0 0 0.0198 Exemplary Glass 125 126 127 128Composition-mol. % P₂O₅ mol. % 65.07 65.48 65.10 64.75 Al₂O₃ mol. %17.29 16.99 17.27 17.50 B₂O₃ mol. % 7.80 7.79 7.80 7.79 Li₂O mol. % 7.743.87 5.73 7.81 TiO₂ mol. % 0 0 0 0 MgO mol. % 2.06 5.83 4.07 2.12 Na₂Omol. % 0 0 0 0 ZrO₂ mol. % 0 0 0 0 CaO mol. % 0.0212 0.0213 0.02120.0211 SiO₂ mol. % 0.0197 0.0198 0.0198 0.0197 Composition constraintsP₂O₅ + B₂O₃ mol. % 73.51 73.30 72.98 73.28 R₂O + RO + SnO₂ + MnO₂ mol. %7.017 6.162 5.010 9.714 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 7.017 6.162 5.010 9.714 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol.% −6.099 −6.059 −6.002 −4.799 Al₂O₃ − R₂O − RO mol. % 10.48 11.55 12.987.275 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 1.975 2.827 4.017 0 Ce₂O₃ + CeO₂ +ZrO₂ R₂O + RO + B₂O₃ mol. % 14.92 14.10 13.00 17.51 Compositionconstraints P₂O₅ + B₂O₃ mol. % 72.87 73.27 72.90 72.54 R₂O + RO + SnO₂ +MnO₂ mol. % 9.821 9.719 9.815 9.941 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 9.821 9.719 9.815 9.941 3 * Al₂O₃ + R₂O + RO− P₂O₅ mol. % −3.396 −4.792 −3.473 −2.321 Al₂O₃ − R₂O − RO mol. % 7.4647.271 7.454 7.557 TiO₂ + La₂O₃ + Y ₂O₃ + mol. % 0 0 0 0 Ce₂O₃ + CeO₂ +ZrO₂ R₂O + RO + B₂O₃ mol. % 17.62 17.51 17.61 17.73 Measured properties15-min devit test (0/1) 1 1 1 1 Measured properties 15-min devit test(0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol. % 1.80731.8902 1.9863 3.0037 P_(E) [for E] GPa 78.31 78.63 79.08 76.52 Predictedand calculated properties I_(B), mol. % 4.4231 3.0022 4.3372 5.4620P_(E) [for E] GPa 75.62 76.55 75.73 74.99 Exemplary Glass 129 130 131132 Composition-mol. % P₂O₅ mol. % 65.48 65.09 64.81 64.46 Al₂O₃ mol. %16.99 17.27 17.47 17.71 B₂O₃ mol. % 7.80 7.79 7.81 7.80 Li₂O mol. % 2.244.18 5.76 7.83 MgO mol. % 7.49 5.64 4.12 2.14 CaO mol. % 0 0.0212 0.02120.0211 SiO₂ mol. % 0 0.0198 0.0198 0.0394 Exemplary Glass 133 134 135136 Composition-mol. % P₂O₅ mol. % 65.07 64.76 64.46 63.72 Al₂O₃ mol. %17.28 17.50 17.72 17.97 B₂O₃ mol. % 7.80 7.80 7.79 7.80 Li₂O mol. % 2.314.02 5.67 8.11 MgO mol. % 7.51 5.89 4.32 2.33 CaO mol. % 0 0.0212 0.02110.021 SiO₂ mol. % 0.0198 0.0198 0.0197 0.0392 Composition constraintsP₂O₅ + B₂O₃ mol. % 73.28 72.88 72.62 72.26 R₂O + RO + SnO₂ + MnO₂ mol. %9.731 9.838 9.899 10.00 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 9.731 9.838 9.899 10.00 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol.% −4.777 −3.452 −2.514 −1.345 Al₂O₃ − R₂O − RO mol. % 7.258 7.428 7.5667.710 R₂O + RO + B₂O₃ mol. % 17.53 17.63 17.70 17.79 Compositionconstraints P₂O₅ + B₂O₃ mol. % 72.88 72.55 72.25 71.53 R₂O + RO + SnO₂ +MnO₂ mol. % 9.822 9.930 10.01 10.46 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 9.822 9.930 10.01 10.46 3 * Al₂O₃ + R₂O + RO− P₂O₅ mol. % −3.400 −2.337 −1.305 0.6520 Al₂O₃ − R₂O − RO mol. % 7.4627.567 7.706 7.508 R₂O + RO + B₂O₃ mol. % 17.63 17.73 17.80 18.27Measured properties 15-min devit test (0/1) 1 1 1 1 Measured properties15-min devit test (0/1) 1 1 1 1 Predicted and calculated propertiesI_(B), mol. % 2.9983 4.3285 5.2909 6.4787 P_(E) [for E] GPa 76.58 75.7475.13 74.37 Predicted and calculated properties I_(B), mol. % 4.40165.4447 6.4887 8.4740 P_(E) [for E] GPa 75.73 75.06 74.42 73.72 ExemplaryGlass 137 138 139 140 Composition-mol. % P₂O₅ mol. % 64.58 64.65 64.2464.23 Al₂O₃ mol. % 17.10 17.10 17.20 17.22 B₂O₃ mol. % 6.43 5.62 5.424.52 Li₂O mol. % 6.92 6.35 6.16 5.50 TiO₂ mol. % 1.14 1.40 1.98 2.34 MgOmol. % 3.72 3.83 4.89 5.17 Na₂O mol. % 0.0762 0.61 0.0761 0.59 ZrO₂ mol.% 0 0.41 0 0.38 CaO mol. % 0.0211 0.0212 0.021 0.0211 SiO₂ mol. % 0.01970.0197 0.0196 0.0197 Exemplary Glass 141 142 143 144 Composition-mol. %P₂O₅ mol. % 64.33 63.87 63.88 63.94 Al₂O₃ mol. % 17.20 17.30 17.31 17.32B₂O₃ mol. % 3.99 4.42 3.55 2.94 Li₂O mol. % 5.17 5.40 4.78 4.36 TiO₂mol. % 2.44 2.82 3.17 3.35 MgO mol. % 5.07 6.08 6.30 6.38 Na₂O mol. %1.03 0.076 0.59 0.98 ZrO₂ mol. % 0.73 0 0.38 0.69 CaO mol. % 0.02120.021 0.0211 0.0211 SiO₂ mol. % 0.0198 0.0196 0.0197 0.0197 Compositionconstraints P₂O₅ + B₂O₃ mol. % 71.01 70.27 69.66 68.75 R₂O + RO + SnO₂ +MnO₂ mol. % 10.74 10.81 11.14 11.28 (Al₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 10.74 10.81 11.14 11.28 3 * Al₂O₃ + R₂O + RO− P₂O₅ mol. % −2.541 −2.548 −1.486 −1.280 Al₂O₃ − R₂O − RO mol. % 6.3626.289 6.060 5.938 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 1.139 1.809 1.979 2.725Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 17.17 16.43 16.56 15.80Composition constraints P₂O₅ + B₂O₃ mol. % 68.32 68.29 67.42 66.88 R₂O +RO + SnO₂ + MnO₂ mol. % 11.29 11.57 11.70 11.74 (Al₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.29 11.57 11.70 11.74 3 *Al₂O₃ + R₂O + RO − P₂O₅ mol. % −1.447 −0.3958 −0.2490 −0.2508 Al₂O₃ −R₂O − RO mol. % 5.911 5.728 5.613 5.578 TiO₂ + La₂O₃ + Y₂O₃ + mol. %3.170 2.816 3.548 4.045 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 15.2815.99 15.24 14.68 Measured properties d_(RT) g/cm³ 2.546 2.532 2.54715-min devit test (0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 2.55415-min devit test (0/1) 1 1 1 1 Predicted and calculated propertiesI_(B), mol. % 3.8888 3.0720 3.9444 3.2257 P_(E) [for E] GPa 75.37 75.4774.98 74.97 Predicted and calculated properties I_(B), mol. % 2.52904.0018 3.2609 2.6843 P_(E) [for E] GPa 75.12 74.56 74.59 74.67 ExemplaryGlass 145 146 147 148 Composition mol. % P₂O₅ mol. % 64.02 63.42 63.4663.50 Al₂O₃ mol. % 17.32 17.44 17.45 17.45 B₂O₃ mol. % 2.34 3.04 2.201.56 La₂O₃ mol. % 0 0 0 0 Li₂O mol. % 3.94 4.37 3.75 3.33 TiO₂ mol. %3.50 3.96 4.25 4.46 MgO mol. % 6.34 7.64 7.79 7.87 Na₂O mol. % 1.460.0948 0.63 1.05 ZrO₂ mol. % 1.05 0 0.42 0.74 CeO₂ mol. % 0 0 0 0 CaOmol. % 0.0212 0.021 0.021 0.0211 SiO₂ mol. % 0.0198 0.0196 0.0196 0.0197Fe₂O₃ mol. % 0 0 0 0 Exemplary Glass 149 150 151 152 Composition mol. %P₂O₅ mol. % 63.54 54.97 54.99 54.98 Al₂O₃ mol. % 17.46 14.00 13.99 14.00B₂O₃ mol. % 0.92 2.00 2.00 2.00 La₂O₃ mol. % 0 3.00 0 3.00 Li₂O mol. %2.86 10.00 10.00 12.99 TiO₂ mol. % 4.68 10.00 10.00 10.00 MgO mol. %7.98 6.00 9.00 3.00 Na₂O mol. % 1.47 0.0102 0.0103 0.0066 ZrO₂ mol. %1.05 0 0 0 CeO₂ mol. % 0 0.0179 0 0.0178 CaO mol. % 0.0212 0.00585.80E−4 0.0056 SiO₂ mol. % 0.0198 0.0039 0.004 0.0039 Fe₂O₃ mol. % 07.30E−5 1.40E−4 7.30E−5 Composition constraints P₂O₅ + B₂O₃ mol. % 66.3666.46 65.67 65.06 R₂O + RO + SnO₂ + MnO₂ mol. % 11.76 12.12 12.19 12.26(Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.7612.12 12.19 12.26 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % −0.3095 1.034 1.0741.123 Al₂O₃ − R₂O − RO mol. % 5.555 5.319 5.263 5.188 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 4.549 3.958 4.675 5.198 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO +B₂O₃ mol. % 14.10 15.16 14.39 13.83 Composition constraints P₂O₅ + B₂O₃mol. % 64.46 56.98 56.99 56.99 R₂O + RO + SnO₂ + MnO₂ mol. % 12.33 16.0119.01 16.01 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 12.33 16.01 19.01 16.01 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.1613.034 5.996 3.010 Al₂O₃ − R₂O − RO mol. % 5.124 −2.011 −5.013 −2.009TiO₂ + La₂O₃ + Y₂O₃ + mol. % 5.729 13.01 10.00 13.01 Ce₂O₃ + CeO₂ + ZrO₂R₂O + RO + B₂O₃ mol. % 13.25 18.01 21.01 18.01 Measured propertiesd_(RT) g/cm³ 2.564 2.539 2.551 E GPa μ NaOH[ISO695] mg/cm² 15-min devittest (0/1) 1 1 1 1 Measured properties d_(RT) g/cm³ 75.570 79.220 76.260E GPa 0.21500 0.21100 0.21700 μ 1.25406 1.40687 1.16778 NaOH[ISO695]mg/cm² 1 15-min devit test (0/1) Predicted and calculated propertiesI_(B), mol. % 2.0055 4.0688 3.2843 2.6824 P_(E) [for E] GPa 74.75 74.9775.10 75.18 Predicted and calculated properties I_(B), mol. % 2.074814.058 7.9954 14.035 P_(E) [for E] GPa 75.26 79.33 78.69 79.28 ExemplaryGlass 153 154 155 156 Composition-mol. % P₂O₅ mol. % 54.99 54.98 54.9962.93 Al₂O₃ mol. % 14.00 13.99 14.00 17.46 B₂O₃ mol. % 2.00 2.00 2.005.92 La₂O₃ mol. % 0 3.00 0 0 Li₂O mol. % 16.00 11.50 13.00 2.94 TiO₂mol. % 10.00 10.00 10.00 0 MgO mol. % 3.00 4.50 6.00 5.19 Na₂O mol. %0.007 0.0085 0.0087 3.74 ZrO₂ mol. % 0 0 0 1.78 CeO₂ mol. % 0 0.0178 0 0CaO mol. % 3.80E−4 0.0056 5.80E−4 0.0212 SiO₂ mol. % 0.0039 0.0039 0.0040.0198 Fe₂O₃ mol. % 6.70E−5 7.30E−5 6.80E−5 0 Exemplary Glass 157 158159 160 Composition-mol. % P₂O₅ mol. % 63.58 62.91 63.54 63.99 Al₂O₃mol. % 17.48 17.45 17.48 17.49 B₂O₃ mol. % 5.21 6.45 5.86 5.19 La₂O₃mol. % 0 0 0 0 Li₂O mol. % 2.75 2.18 1.87 1.88 TiO₂ mol. % 0 0 0 0 MgOmol. % 5.09 5.97 5.99 5.83 Na₂O mol. % 2.65 3.75 2.73 1.85 ZrO₂ mol. %1.78 1.25 1.18 1.26 CeO₂ mol. % 0 0 0 0 CaO mol. % 1.45 0.0211 1.34 2.49SiO₂ mol. % 0.0198 0.0197 0.0198 0.0199 Fe₂O₃ mol. % 0 0 0 0 Compositionconstraints P₂O₅ + B₂O₃ mol. % 56.99 56.98 56.99 68.85 R₂O + RO + SnO₂ +MnO₂ mol. % 19.01 16.01 19.01 11.88 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.0001.000 1.000 R₂O + RO mol. % 19.01 16.01 19.01 11.88 3 * Al₂O₃ + R₂O + RO− P₂O₅ mol. % 6.005 3.009 6.001 1.330 Al₂O₃ − R₂O − RO mol. % −5.009−2.015 −5.011 5.575 TiO₂ + La₂O₃ + Y₂O₃ + Ce₂O₃ + mol. % 10.00 13.0110.00 1.783 CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 21.01 18.01 21.01 17.80Composition constraints P₂O₅ + B₂O₃ mol. % 68.78 69.36 69.40 69.18 R₂O +RO + SnO₂ + MnO₂ mol. % 11.94 11.92 11.93 12.05 (Li₂O + Na₂O)/R₂O mol. %1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.94 11.92 11.93 12.05 3 *Al₂O₃ + R₂O + RO − P₂O₅ mol. % 0.8015 1.348 0.8226 0.5364 Al₂O₃ − R₂O −RO mol. % 5.539 5.527 5.553 5.448 TiO₂ + La₂O₃ + Y₂O₃ + Ce₂O₃ + mol. %1.780 1.250 1.178 1.259 CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 17.15 18.3717.79 17.24 Measured properties E GPa 79.150 76.260 79.500 μ 0.212000.21800 0.21400 α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ 67.400 69.200 NaOH[ISO695] mg/cm²1.43833 1.2234 1.26623 1 15-min devit test (0/1) Measured properties EGPa μ α²⁰⁻³⁰⁰ × 10⁷ K⁻¹ NaOH[ISO695] mg/cm² 15-min devit test (0/1) 1 11 1 Predicted and calculated properties I_(B), mol. % 8.0057 14.0338.0010 7.2629 P_(E) [for E] GPa 78.59 79.30 78.64 73.33 Predicted andcalculated properties I_(B), mol. % 5.9895 7.7611 6.6703 5.7377 P_(E)[for E] GPa 73.66 73.04 73.31 73.65 Exemplary Glass 161 162 163 164Composition-mol. % P₂O₅ mol. % 62.93 63.54 63.96 64.24 Al₂O₃ mol. %17.46 17.48 17.50 17.50 B₂O₃ mol. % 6.97 6.36 5.85 5.20 Li₂O mol. % 1.391.11 1.00 1.08 MgO mol. % 6.75 6.75 6.71 6.62 Na₂O mol. % 3.74 2.72 1.961.08 ZrO₂ mol. % 0.72 0.67 0.67 0.73 CaO mol. % 0.0211 1.33 2.36 3.55SiO₂ mol. % 0.0197 0.0198 0 0 Exemplary Glass 165 166 167 168Composition-mol. % P₂O₅ mol. % 62.95 63.61 64.00 64.25 Al₂O₃ mol. %17.45 17.49 17.51 17.50 B₂O₃ mol. % 7.70 6.98 6.44 5.91 Li₂O mol. % 0.320.0794 0 0 MgO mol. % 7.82 7.74 7.70 7.70 Na₂O mol. % 3.73 2.64 1.841.06 ZrO₂ mol. % 0 0 0 0 CaO mol. % 0.0211 1.46 2.52 3.58 SiO₂ mol. % 00 0 0 Composition constraints P₂O₅ + B₂O₃ mol. % 69.90 69.90 69.81 69.45R₂O + RO + SnO₂ + MnO₂ mol. % 11.90 11.92 12.02 12.33 (Li₂O + Na₂O)/R₂Omol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.90 11.92 12.02 12.333 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.343 0.8283 0.5723 0.5812 Al₂O₃ −R₂O − RO mol. % 5.553 5.568 5.486 5.172 TiO₂ + La₂O₃ + Y₂O₃ + mol. %0.7203 0.6747 0.6667 0.7254 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. %18.87 18.28 17.87 17.53 Composition constraints P₂O₅ + B₂O₃ mol. % 70.6570.59 70.44 70.16 R₂O + RO + SnO₂ + MnO₂ mol. % 11.89 11.92 12.06 12.34(Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. % 11.8911.92 12.06 12.34 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.303 0.7750 0.57140.5745 Al₂O₃ − R₂O − RO mol. % 5.559 5.575 5.448 5.155 TiO₂ + La₂O₃ +Y₂O₃ + mol. % 0 0 0 0 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 19.5918.90 18.49 18.25 Measured properties 15-min devit test (0/1) 1 1 1 1Measured properties 15-min devit test (0/1) 1 1 1 1 Predicted andcalculated properties I_(B), mol. % 8.3010 7.1907 6.4184 5.7755 P_(E)[for E] GPa 72.76 73.04 73.29 73.70 Predicted and calculated propertiesI_(B), mol. % 8.9932 7.7442 7.0088 6.4724 P_(E) [for E] GPa 72.36 72.7172.99 73.32 Exemplary Glass 169 170 171 172 Composition mol. % P₂O₅ mol.% 63.29 60.25 61.92 63.80 Al₂O₃ mol. % 17.37 16.35 16.21 16.22 B₂O₃ mol.% 7.00 11.13 11.30 10.97 Li₂O mol. % 7.18 7.14 6.71 6.30 MgO mol. % 5.095.07 3.82 2.66 CaO mol. % 0.0208 0.0204 0.0207 0.021 SiO₂ mol. % 0.03880.038 0.0193 0.0196 Exemplary Glass 173 174 175 176 Composition mol. %P₂O₅ mol. % 59.00 60.68 62.11 57.37 Al₂O₃ mol. % 15.93 15.81 15.76 15.38B₂O₃ mol. % 12.79 12.91 12.89 14.98 Li₂O mol. % 7.15 6.69 6.34 7.14 MgOmol. % 5.08 3.85 2.86 5.07 CaO mol. % 0.0202 0.0205 0.0207 0.0199 SiO₂mol. % 0.0377 0.0382 0.0194 0.0372 Composition constraints P₂O₅ + B₂O₃mol. % 70.30 71.38 73.22 74.78 R₂O + RO + SnO₂ + MnO₂ mol. % 12.30 12.2310.55 8.982 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + ROmol. % 12.30 12.23 10.55 8.982 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % 1.1031.020 −2.722 −6.154 Al₂O₃ − R₂O − RO mol. % 5.069 4.112 5.663 7.239R₂O + RO + B₂O₃ mol. % 19.30 23.37 21.85 19.96 Composition constraintsP₂O₅ + B₂O₃ mol. % 71.78 73.60 75.00 72.35 R₂O + RO + SnO₂ + MnO₂ mol. %12.25 10.55 9.219 12.24 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 12.25 10.55 9.219 12.24 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol.% 1.045 −2.692 −5.609 0.9907 Al₂O₃ − R₂O − RO mol. % 3.676 5.259 6.5413.140 R₂O + RO + B₂O₃ mol. % 25.04 23.47 22.11 27.21 Measured properties15-min devit test (0/1) 1 1 1 1 Measured properties 15-min devit test(0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol. % 8.093412.164 8.5653 4.8143 P_(E) [for E] GPa 73.46 74.22 75.81 78.03 Predictedand calculated properties I_(B), mol. % 13.825 10.227 7.2730 15.949P_(E) [for E] GPa 74.53 76.09 78.03 74.93 Exemplary Glass 177 178 179180 Composition-mol. % P₂O₅ mol. % 59.28 63.60 63.60 63.60 Al₂O₃ mol. %15.30 17.50 17.50 17.50 B₂O₃ mol. % 14.96 7.20 7.20 7.20 Li₂O mol. %6.66 3.40 5.40 2.40 TiO₂ mol. % 0 0 0 0 MgO mol. % 3.75 8.30 6.30 9.30CaO mol. % 0.0203 0 0 0 SiO₂ mol. % 0.0378 0 0 0 Exemplary Glass 181 182183 184 Composition-mol. % P₂O₅ mol. % 64.20 63.10 64.60 60.01 Al₂O₃mol. % 18.00 17.00 17.00 16.00 B₂O₃ mol. % 7.20 7.20 4.20 6.00 Li₂O mol.% 5.00 5.00 4.40 3.99 TiO₂ mol. % 0 0 0 8.00 MgO mol. % 5.60 7.70 9.806.00 CaO mol. % 0 0 0 0 SiO₂ mol. % 0 0 0 0 Composition constraintsP₂O₅ + B₂O₃ mol. % 74.23 70.80 70.80 70.80 R₂O + RO + SnO₂ + MnO₂ mol. %10.43 11.70 11.70 11.70 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000R₂O + RO mol. % 10.43 11.70 11.70 11.70 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol.% −2.953 0.6075 0.5904 0.5858 Al₂O₃ − R₂O − RO mol. % 4.868 5.804 5.7955.798 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 0 0 0 0 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 25.39 18.90 18.90 18.90 Composition constraints P₂O₅ +B₂O₃ mol. % 71.40 70.30 68.80 66.01 R₂O + RO + SnO₂ + MnO₂ mol. % 10.6012.70 14.20 9.99 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O +RO mol. % 10.60 12.70 14.20 9.99 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %0.3961 0.6133 0.6090 −2.013 Al₂O₃ − R₂O − RO mol. % 7.396 4.304 2.8006.013 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 0 0 0 7.997 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 17.80 19.90 18.40 15.99 Measured properties Tg ° C.15-min devit test (0/1) 1 1 1 1 Measured properties Tg ° C. 571 15-mindevit test (0/1) 1 1 1 Predicted and calculated properties I_(B), mol. %12.008 7.8065 7.7909 7.7867 P_(E) [for E] GPa 76.65 73.49 73.45 73.50Predicted and calculated properties I_(B), mol. % 7.5956 7.8128 4.80953.9875 P_(E) [for E] GPa 73.55 73.32 72.56 79.03 Exemplary Glass 185 186187 188 Composition-mol. % P₂O₅ mol. % 59.98 60.00 60.01 55.00 Al₂O₃mol. % 16.00 15.99 12.00 12.00 B₂O₃ mol. % 9.00 6.00 7.50 7.50 Li₂O mol.% 4.02 6.99 7.49 7.49 TiO₂ mol. % 5.00 5.00 3.00 5.01 MgO mol. % 6.016.01 10.00 6.52 Na₂O mol. % 0 0 0 0 CaO mol. % 0 0 0 6.49 K₂O mol. % 0 00 0 Exemplary Glass 189 190 191 192 Composition-mol. % P₂O₅ mol. % 65.5364.70 64.69 64.64 Al₂O₃ mol. % 16.97 20.00 19.43 18.83 B₂O₃ mol. % 7.815.03 5.04 5.05 Li₂O mol. % 0.28 0 0 0 TiO₂ mol. % 0 5.02 5.02 5.02 MgOmol. % 5.37 0.18 0.76 1.39 Na₂O mol. % 3.04 5.06 5.06 5.07 CaO mol. % 00 0 0 K₂O mol. % 1.00 0 0 0 Composition constraints P₂O₅ + B₂O₃ mol. %68.98 66.00 67.51 62.50 R₂O + RO + SnO₂ + MnO₂ mol. % 10.03 13.00 17.4920.50 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. %10.03 13.00 17.49 20.50 K₂O + Rb₂O + CS₂O mol. % 0 0 0 0 3 * Al₂O₃ +R₂O + RO − P₂O₅ mol. % −1.966 0.9884 −6.514 1.483 Al₂O₃ − R₂O − RO mol.% 5.972 2.993 −5.489 −8.498 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 4.997 5.0042.997 5.006 Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 19.02 19.00 24.9927.99 Composition constraints P₂O₅ + B₂O₃ mol. % 73.34 69.74 69.73 69.69R₂O + RO + SnO₂ + MnO₂ mol. % 9.690 5.241 5.824 6.460 (Li₂O + Na₂O)/R₂Omol. % 0.7687 1.000 1.000 1.000 R₂O + RO mol. % 9.690 5.241 5.824 6.460K₂O + Rb₂O + CS₂O mol. % 1.000 0 0 0 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %−4.936 0.5528 −0.5835 −1.670 Al₂O₃ − R₂O − RO mol. % 7.278 14.76 13.6112.37 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 0 5.018 5.018 5.016 Ce₂O₃ + CeO₂ +ZrO₂ R₂O + RO + B₂O₃ mol. % 17.50 10.27 10.86 11.51 Measured propertiesd_(RT) g/cm³ E GPa E/d_(RT) GPa · cm³/g T_(g) ° C. 570 529 520 49815-min devit test (0/1) Measured properties d_(RT) g/cm³ 2.549 E GPa86.400 E/d_(RT) GPa · cm³/g 33.900 T_(g) ° C. 15-min devit test (0/1) 11 1 1 Predicted and calculated properties I_(B), mol. % 7.0309 6.99220.98684 8.9804 P_(E) [for E] GPa 77.87 75.97 78.06 76.29 Predicted andcalculated properties I_(B), mol. % 2.8498 5.5912 4.4465 3.5957 P_(E)[for E] GPa 74.73 74.90 74.99 75.56 Exemplary Glass 193 194 195 196Composition-mol. % P₂O₅ mol. % 64.64 64.62 64.60 64.55 Al₂O₃ mol. %18.40 17.99 17.58 17.14 B₂O₃ mol. % 5.04 5.05 5.06 5.06 Li₂O mol. % 0 00 0 TiO₂ mol. % 5.02 5.01 5.01 5.02 MgO mol. % 1.85 2.26 2.68 3.15 Na₂Omol. % 5.05 5.06 5.07 5.08 Exemplary Glass 197 198 199 200Composition-mol. % P₂O₅ mol. % 64.54 64.50 65.01 65.00 Al₂O₃ mol. %16.58 16.04 18.00 18.58 B₂O₃ mol. % 5.06 5.06 5.00 5.00 Li₂O mol. % 0 05.00 5.00 TiO₂ mol. % 5.02 5.02 5.00 5.00 MgO mol. % 3.71 4.30 2.00 1.42Na₂O mol. % 5.08 5.09 0 0 Composition constraints P₂O₅ + B₂O₃ mol. %69.68 69.67 69.65 69.61 R₂O + RO + SnO₂ + MnO₂ mol. % 6.899 7.328 7.7528.232 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O + RO mol. %6.899 7.328 7.752 8.232 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. % −2.543 −3.316−4.103 −4.887 Al₂O₃ − R₂O − RO mol. % 11.50 10.66 9.829 8.912 TiO₂ +La₂O₃ + Y₂O₃ + mol. % 5.021 5.010 5.014 5.016 Ce₂O₃ + CeO₂ + ZrO₂ R₂O +RO + B₂O₃ mol. % 11.94 12.38 12.81 13.29 Composition constraints P₂O₅ +B₂O₃ mol. % 69.60 69.56 70.00 70.00 R₂O + RO + SnO₂ + MnO₂ mol. % 8.7959.385 7.000 6.420 (Li₂O + Na₂O)/R₂O mol. % 1.000 1.000 1.000 1.000 R₂O +RO mol. % 8.795 9.385 7.000 6.420 3 * Al₂O₃ + R₂O + RO − P₂O₅ mol. %−5.998 −7.002 −4.019 −2.836 Al₂O₃ − R₂O − RO mol. % 7.788 6.652 11.0012.16 TiO₂ + La₂O₃ + Y₂O₃ + mol. % 5.016 5.016 4.999 5.000 Ce₂O₃ +CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 13.86 14.45 12.00 11.42 Measuredproperties 15-min devit test (0/1) 1 1 1 1 Measured properties 15-mindevit test (0/1) 1 1 1 1 Predicted and calculated properties I_(B), mol.% 2.7639 1.7552 0.94025 0.15813 P_(E) [for E] GPa 76.02 76.41 76.8277.22 Predicted and calculated properties I_(B), mol. % −0.95213 −1.93700.98071 2.1637 P_(E) [for E] GPa 76.96 76.57 78.75 78.13 Exemplary Glass201 202 203 204 Composition-mol. % P₂O₅ mol. % 64.99 65.00 65.00 65.00Al₂O₃ mol. % 17.42 19.00 16.99 19.43 B₂O₃ mol. % 5.00 5.00 5.00 5.00Li₂O mol. % 5.00 5.00 5.00 5.00 TiO₂ mol. % 5.00 5.00 5.00 5.00 MgO mol.% 2.58 1.00 3.01 0.57 CaO mol. % 0 0 0 0 205 206 207 208 209Composition-mol. % P₂O₅ mol. % 64.99 65.00 65.00 63.99 66.21 Al₂O₃ mol.% 16.57 20.00 16.00 19.25 17.00 B₂O₃ mol. % 5.00 5.00 5.00 7.55 7.80Li₂O mol. % 5.00 5.00 5.00 7.44 0 TiO₂ mol. % 5.00 5.00 5.00 0 0 MgOmol. % 3.43 0 4.00 0 8.99 CaO mol. % 0 0 0 1.78 0 Compositionconstraints P₂O₅ + B₂O₃ mol. % 69.99 70.00 70.00 70.00 RO + RO + SnO₂ +mol. % 7.584 5.997 8.009 5.571 MnO₂ (Li₂O + NaO)/ mol. % 1.000 1.0001.000 1.000 R₂O R₂O + RO mol. % 7.584 5.997 8.009 5.571 3 * Al₂O₃ +R₂O + mol. % −5.142 −2.004 −6.032 −1.125 RO − P₂O₅ Al₂O₃ − R₂O − RO mol.% 9.839 13.00 8.978 13.86 TiO₂ + La₂O₃ + mol. % 4.999 5.001 5.001 4.999Y₂O₃ + Ce₂O₃ + CeO₂ + ZrO₂ R₂O + RO + B₂O₃ mol. % 12.58 11.00 13.0110.57 Composition constraints P₂O₅ + B₂O₃ mol. % 69.99 70.00 70.00 71.5474.01 RO + RO + SnO₂ + mol. % 8.433 4.998 9.001 9.219 8.990 MnO₂ (Li₂O +NaO)/ mol. % 1.000 1.000 1.000 1.000 0 R₂O R₂O + RO mol. % 8.433 4.9989.001 9.219 8.990 3 * Al₂O₃ + R₂O + mol. % −6.844 0.01023 −8.003 2.969−6.215 RO − P₂O₅ Al₂O₃ − R₂O − RO mol. % 8.140 15.01 6.998 10.03 8.011TiO₂ + La₂O₃ + mol. % 5.000 5.000 5.000 0 0 Y₂O₃ + Ce₂O₃ + CeO₂ + ZrO₂R₂O + RO + B₂O₃ mol. % 13.43 10.00 14.00 16.77 16.79 Measured properties_(dRT) g/cm³ E GPa μ E/d_(RT) GPa · cm³/g n_(d) v_(d) T_(liq) ° C.HCl[DIN12116] mg/cm² NaOH[ISO695] mg/cm² Weathering- mg/cm² 85° C./85%RH vHF loss mg/cm² vHF appearance 15-min devit test (0/1) 1 1 1 1 1Measured properties _(dRT) g/cm³ 2.565 E GPa 84.257 μ 0.20100 E/d_(RT)GPa · cm³/g 32.850 n_(d) 1.5281 v_(d) 71.4 T_(liq) ° C. 1180HCl[DIN12116] mg/cm² 1.42 NaOH[ISO695] mg/cm² 53.5 Weathering- mg/cm²0.05 85° C./85% RH vHF loss mg/cm² 0.13 vHF appearance clear. shiny15-min devit test (0/1) 1 1 1 1 1 Predicted and calculated propertiesI_(B), mol. % −0.14182 2.9962 −1.0319 3.8740 P_(E) [for E] GPa 79.2177.69 78.88 77.23 Predicted and calculated properties I_(B), mol. %−1.8439 5.0099 −3.0032 10.520 1.5979 P_(E) [for E] GPa 78.57 76.64 78.1374.83 77.56

FIG. 3 shows the relationship between the Young's modulus E and theratio P₂O₅/(3*Al₂O₃+B₂O₃) for the Exemplary Glasses of Table 6 for whichYoung's modulus was measured. As follows from the figure, the highestvalues of the Young's modulus were observed in the case when theindicated ratio is in the range from about 0.95 to about 1.30, or in therange from 0.95 to about 1.20, or in the range from about 1.00 to about1.15.

Glasses according to the present disclosure have a Young's modulus Egreater than 70 GPa, or greater than 80 GPa, or greater than 90 GPa, orgreater than 100 GPa, or greater than 110 GPa, or in a range from 70 GPato 120 GPa, or in a range from 75 GPa to 115 GPa, or in a range from 80GPa to 110 GPa.

Glasses according to the present disclosure have a value of theparameter P_(E) greater than 70 GPa, or greater than 80 GPa, or greaterthan 90 GPa, or greater than 100 GPa, or greater than 110 GPa, or in arange from 70 GPa to 120 GPa, or in a range from 75 GPa to 115 GPa, orin a range from 80 GPa to 110 GPa.

The following non-limiting aspects are encompassed by the presentdisclosure. To the extent not already described, any one of the featuresof the first through the sixty-first aspect may be combined in part orin whole with features of any one or more of the other aspects of thepresent disclosure to form additional aspects, even if such acombination is not explicitly described.

According to a first aspect, the glass comprises a plurality ofcomponents, the glass having a composition of the components comprisinggreater than or equal to 0.3 mol. % and less than or equal to 50.0 mol.% B₂O₃, greater than or equal to 0.0 mol. % and less than or equal to75.0 mol. % P₂O₅, greater than or equal to 0.5 mol. % and less than orequal to 15.0 mol. % MgO, greater than or equal to 0.0 mol. % and lessthan or equal to 30.0 mol. % Al₂O₃, greater than or equal to 0.0 mol. %and less than or equal to 1.0 mol. % Cu₂O+CuO, greater than or equal to0.3 mol. % and less than or equal to 15.0 mol. % R₂O, greater than orequal to 0.0 at. % and less than or equal to 0.5 at. % F, greater thanor equal to 15.0 mol. % and less than or equal to 75.0 mol. % P₂O₅+B₂O₃,greater than or equal to 0.8 mol. % and less than or equal to 15.0 mol.% R₂O+RO+SnO₂+MnO₂ and greater than or equal to 0.0 mol. % and less thanor equal to 5.0 mol. % TeO₂+GeO₂, wherein the composition of thecomponents is substantially free of SiO₂ and substantially free of PbOand wherein the composition of the components satisfies the conditions:(Li₂O+Na₂O)/R₂O [mol. %]≥0.75, where R₂O is a total sum of monovalentmetal oxides, and RO is a total sum of divalent metal oxides.

According to a second aspect, the glass of the first aspect, wherein thecomposition of the components comprises greater than or equal to 60.0mol. % and less than or equal to 68.0 mol. % P₂O₅, greater than or equalto 15.0 mol. % and less than or equal to 20.0 mol. % Al₂O₃, greater thanor equal to 0.3 mol. % and less than or equal to 12.0 mol. % B₂O₃,greater than or equal to 1.0 mol. % and less than or equal to 15.0 mol.% R₂O+RO and wherein the composition of the components satisfies thecondition: 0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol. %]≤1.20.

According to a third aspect, the glass of any aspect 1, wherein thecomposition of the components comprises greater than or equal to 48.0mol. % and less than or equal to 75.0 mol. % P₂O₅, greater than or equalto 8.0 mol. % and less than or equal to 30.0 mol. % Al₂O₃, greater thanor equal to 0.3 mol. % and less than or equal to 40.0 mol. %Alk₂O+MgO+RE_(m)O_(n), greater than or equal to 0.25 mol. % and lessthan or equal to 40 mol. % TiO₂+ZrO₂ and greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % Na₂O+K₂O+BaO and whereinthe composition of the components is substantially free of Cu, Co, Ni,Cr, V and Bi, where Alk₂O is a total sum of alkali metal oxides, andRE_(m)O_(n) is a total sum of rare earth metal oxides.

According to a fourth aspect, the glass of any one of aspects 1-3,wherein the glass has a batch index, I_(B) that is greater than or equalto 0.000, where I_(B) is calculated from the glass composition in termsof mol. % of the components according to the Formula (I):

I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅,  (I).

According to a fifth aspect, the glass of any one of aspects 1-4,wherein the composition of the components satisfies the condition:−1≤min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO)) K≤12, whereRE_(m)O_(n) is a total sum of rare earth metal oxides, and R₂O is atotal sum of monovalent metal oxides.

According to a sixth aspect, the glass of any one of aspects 1 and 3-5,wherein the composition of the components comprises greater than orequal to 50.0 mol. % and less than or equal to 70.0 mol. % P₂O₅, greaterthan or equal to 10.0 mol. % and less than or equal to 30.0 mol. %Al₂O₃, greater than or equal to 0.5 mol. % and less than or equal to10.0 mol. % MgO, greater than or equal to 0.3 mol. % and less than orequal to 10.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and lessthan or equal to 15.0 mol. % TiO₂, greater than or equal to 0.0 mol. %and less than or equal to 10.0 mol. % CeO₂, greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % K₂O, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % Li₂O, greater thanor equal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O,greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %La₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 7.5mol. % Y₂O₃, greater than or equal to 0.0 mol. % and less than or equalto 4.0 mol. % CaO and greater than or equal to 0.0 mol. % and less thanor equal to 4.0 mol. % ZrO₂.

According to a seventh aspect, the glass of any one of aspects 1 and3-6, wherein the composition of the components comprises one or more ofthe following: greater than or equal to 53.5 mol. % and less than orequal to 66.0 mol. % P₂O₅, greater than or equal to 15.5 mol. % and lessthan or equal to 28.5 mol. % Al₂O₃, greater than or equal to 0.75 mol. %and less than or equal to 7.25 mol. % MgO, greater than or equal to 0.5mol. % and less than or equal to 8.0 mol. % B₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 11.0 mol. % TiO₂, greater thanor equal to 0.0 mol. % and less than or equal to 9.0 mol. % K₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 9.0 mol. % Li₂O,greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5mol. % CeO₂, greater than or equal to 0.0 mol. % and less than or equalto 5.5 mol. % La₂O₃, greater than or equal to 0.0 mol. % and less thanor equal to 5.5 mol. % Y₂O₃, greater than or equal to 0.0 mol. % andless than or equal to 4.0 mol. % CaO, greater than or equal to 0.0 mol.% and less than or equal to 3.6 mol. % ZrO₂ and greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. % Nd₂O₃.

According to an eighth aspect, the glass of any one of aspects 1 and3-7, wherein the composition of the components comprises greater than orequal to 58.0 mol. % and less than or equal to 66.0 mol. % P₂O₅, greaterthan or equal to 16.0 mol. % and less than or equal to 27.0 mol. %Al₂O₃, greater than or equal to 1.5 mol. % and less than or equal to 7.8mol. % B₂O₃, greater than or equal to 1.5 mol. % and less than or equalto 6.3 mol. % MgO, greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and lessthan or equal to 8.0 mol. % K₂O, greater than or equal to 0.0 mol. % andless than or equal to 8.0 mol. % Li₂O, greater than or equal to 0.0 mol.% and less than or equal to 8.0 mol. % Na₂O, greater than or equal to 0mol. % and less than or equal to 5.75 mol. % CeO₂, greater than or equalto 0 mol. % and less than or equal to 4.75 mol. % La₂O₃, greater than orequal to 0 mol. % and less than or equal to 4.75 mol. % Y₂O₃, greaterthan or equal to 0.0 mol. % and less than or equal to 3.4 mol. % CaO,greater than or equal to 0.0 mol. % and less than or equal to 3.2 mol. %ZrO₂ and greater than or equal to 0.0 mol. % and less than or equal to1.5 mol. % Nd₂O₃.

According to a ninth aspect, the glass of any one of aspects 1-8,wherein the composition of the components comprises greater than orequal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅, greaterthan or equal to 0.0 mol. % and less than or equal to 1.0 mol. % BaO,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %V₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 3.0mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % and lessthan or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition of thecomponents is substantially free of Cu, Co, Ni, Cr, V and Bi andsubstantially free of fluorine.

According to a tenth aspect, the glass of any one of aspects 1-9,wherein the glass has logarithm of liquidus viscosity, Log(η_(liq), [P])that is greater than or equal to 2.0.

According to an eleventh aspect, the glass of any one of aspects 1-10,wherein the glass has one or more of the following attributes: a massdifference per unit area in HCl according to DIN12116, HCl[DIN12116],that is less than or equal to 10 mg/cm² and a mass difference per unitarea in NaOH according to ISO695, NaOH[ISO695], that is less than orequal to 100 mg/cm².

According to a twelfth aspect, the glass of any one of aspects 1-11,wherein the glass has vHF mass difference per unit area that is lessthan or equal to 1.0 mg/cm².

According to a thirteenth aspect, the glass of any one of aspects 1, 3-5and 9-12, wherein the composition of the components comprises greaterthan or equal to 30.0 mol. % and less than or equal to 75.0 mol. % P₂O₅,greater than or equal to 8.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.0 mol. % and less than or equal to14.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than orequal to 8.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 5.0 mol. % K₂O, greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % BaO, greater than or equal to 0.5 mol.% and less than or equal to 15.0 mol. % La₂O₃+CeO₂+Ce₂O₃, greater thanor equal to 0.5 mol. % and less than or equal to 15.0 mol. %Li₂O+Na₂O+MgO+CaO and greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. % Bi₂O₃+Cu₂O+CuO and wherein the composition of thecomponents satisfies the condition: (La₂O₃+CeO₂+Ce₂O₃)/RE_(m)O_(n) [mol.%]≥0.51, where RE_(m)O_(n) is a total sum of rare earth metal oxides.

According to a fourteenth aspect, the glass of any one of aspects 1-13,wherein the glass satisfies the conditions: P_(E)>75, where P_(E) iscalculated from the glass composition in terms of mol. % of thecomponents according to the Formula (II):

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II)

According to a fifteenth aspect, the glass of any one of aspects 1-14,wherein the glass has a Young's modulus, E that is greater than or equalto 75 GPa.

According to a sixteenth aspect, the glass of the fifteenth aspect,wherein the glass has a Young's modulus, E that is greater than or equalto 80 GPa.

According to a seventeenth aspect, the glass of the sixteenth aspect,wherein the glass has a Young's modulus, E that is greater than or equalto 85 GPa.

According to an eighteenth aspect, the glass of the seventeenth aspectany of the aspects 14-17, wherein P_(E)>85.

According to a nineteenth aspect, the glass of any one of aspects 1-18,wherein the glass has an average linear thermal expansion coefficient ofglass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that is greater than or equalto 60 K⁻¹, and less than or equal to 70 K⁻¹.

According to a twentieth aspect, the glass of the nineteenth aspect,wherein the glass has an average linear thermal expansion coefficient ofglass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that is greater than or equalto 63 K⁻¹, and less than or equal to 67 K⁻¹.

According to a twenty-first aspect, the glass comprises a plurality ofcomponents, the glass having a composition of the components comprisinggreater than or equal to 40.0 mol. % and less than or equal to 75.0 mol.% P₂O₅, greater than or equal to 0.5 mol. % and less than or equal to10.5 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than orequal to 25.0 mol. % Al₂O₃, greater than or equal to 0.0 mol. % and lessthan or equal to 0.5 mol. % SiO₂, greater than or equal to 0.0 at. % andless than or equal to 5.0 at. % F, greater than or equal to 0.5 mol. %R₂O+RO, greater than or equal to 0.0 mol. % and less than or equal to9.5 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 0.5 mol. % ZnO+CuO+Cu₂O, wherein the compositionof the components satisfies the conditions: 3*Al₂O₃+R₂O+RO−P₂O₅[mol.%]≥−7.0 and Al₂O₃−R₂O−RO [mol. %]≥7.95.

According to a twenty-second aspect, the glass of the twenty-firstaspect, wherein the composition of the components comprises greater thanor equal to 60.0 mol. % and less than or equal to 68.0 mol. % P₂O₅,greater than or equal to 15.0 mol. % and less than or equal to 20.0 mol.% Al₂O₃, greater than or equal to 0.5 mol. % and less than or equal to12.0 mol. % B₂O₃, greater than or equal to 1.0 mol. % and less than orequal to 15.0 mol. % R₂O+RO and wherein the composition of thecomponents satisfies the conditions: 0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol.%]≤1.20, where R₂O is a total sum of monovalent metal oxides, and RO isa total sum of divalent metal oxides.

According to a twenty-third aspect, the glass of aspect 21, wherein thecomposition of the components comprises greater than or equal to 48.0mol. % and less than or equal to 75.0 mol. % P₂O₅, greater than or equalto 8.0 mol. % and less than or equal to 30.0 mol. % Al₂O₃, greater thanor equal to 0.0 mol. % and less than or equal to 3.0 mol. % SiO₂,greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol.% RO, greater than or equal to 0.3 mol. % and less than or equal to 40.0mol. % Alk₂O+MgO+RE_(m)O_(n), greater than or equal to 0.25 mol. % andless than or equal to 40 mol. % TiO₂+ZrO₂ and greater than or equal to0.0 mol. % and less than or equal to 10.0 mol. % Na₂O+K₂O+BaO andwherein the composition of the components is substantially free of Cu,Co, Ni, Cr, V and Bi, where Alk₂O is a total sum of alkali metal oxides,RE_(m)O_(n) is a total sum of rare earth metal oxides, and RO is a totalsum of divalent metal oxides.

According to a twenty-fourth aspect, the glass of any one of aspects21-23, wherein the glass has a batch index, I_(B) that is greater thanor equal to 0.000, where I_(B) is calculated from the glass compositionin terms of mol. % of the components according to the Formula (I):

I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅,  (I).

According to a twenty-fifth aspect, the glass of any one of aspects21-24, wherein the composition of the components satisfies thecondition: −1≤min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))≤12,where RE_(m)O_(n) is a total sum of rare earth metal oxides, and R₂O isa total sum of monovalent metal oxides.

According to a twenty-sixth aspect, the glass of any one of aspects 21or 23-25, wherein the composition of the components comprises greaterthan or equal to 50.0 mol. % and less than or equal to 70.0 mol. % P₂O₅,greater than or equal to 10.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.5 mol. % and less than or equal to10.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than orequal to 15.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % CeO₂, greater than or equal to 0.0 mol. %and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % Li₂O, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % MgO, greater than orequal to 0.0 mol. % and less than or equal to 7.5 mol. % La₂O₃, greaterthan or equal to 0.0 mol. % and less than or equal to 7.5 mol. % Y₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 4.0 mol. %CaO and greater than or equal to 0.0 mol. % and less than or equal to4.0 mol. % ZrO₂.

According to a twenty-seventh aspect, the glass of any one of aspects 21or 23-26, wherein the composition of the components comprises one ormore of the following components: greater than or equal to 53.5 mol. %and less than or equal to 66.0 mol. % P₂O₅, greater than or equal to15.5 mol. % and less than or equal to 28.5 mol. % Al₂O₃, greater than orequal to 0.75 mol. % and less than or equal to 7.25 mol. % MgO, greaterthan or equal to 0.5 mol. % and less than or equal to 8.0 mol. % B₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 11.0 mol.% TiO₂, greater than or equal to 0.0 mol. % and less than or equal to9.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than orequal to 9.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 9.0 mol. % Na₂O, greater than or equal to 0.0 mol. %and less than or equal to 6.5 mol. % CeO₂, greater than or equal to 0.0mol. % and less than or equal to 5.5 mol. % La₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 5.5 mol. % Y₂O₃, greater than orequal to 0.0 mol. % and less than or equal to 4.0 mol. % CaO, greaterthan or equal to 0.0 mol. % and less than or equal to 3.6 mol. % ZrO₂and greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % Nd₂O₃.

According to a twenty-eighth aspect, the glass of any one of aspects 21or 23-27, wherein the composition of the components comprises greaterthan or equal to 58.0 mol. % and less than or equal to 66.0 mol. % P₂O₅,greater than or equal to 16.0 mol. % and less than or equal to 27.0 mol.% Al₂O₃, greater than or equal to 1.5 mol. % and less than or equal to7.8 mol. % B₂O₃, greater than or equal to 1.5 mol. % and less than orequal to 6.3 mol. % MgO, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % TiO₂, greater than or equal to 0.0 mol. %and less than or equal to 8.0 mol. % K₂O, greater than or equal to 0.0mol. % and less than or equal to 8.0 mol. % Li₂O, greater than or equalto 0.0 mol. % and less than or equal to 8.0 mol. % Na₂O, greater than orequal to 0 mol. % and less than or equal to 5.75 mol. % CeO₂, greaterthan or equal to 0 mol. % and less than or equal to 4.75 mol. % La₂O₃,greater than or equal to 0 mol. % and less than or equal to 4.75 mol. %Y₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 3.4mol. % CaO, greater than or equal to 0.0 mol. % and less than or equalto 3.2 mol. % ZrO₂ and greater than or equal to 0.0 mol. % and less thanor equal to 1.5 mol. % Nd₂O₃.

According to a twenty-ninth aspect, the glass of any one of aspects21-28, wherein the composition of the components comprises greater thanor equal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %BaO, greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % V₂O₅, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition ofthe components is substantially free of Cu, Co, Ni, Cr, V and Bi,substantially free of fluorine, substantially free of PbO andsubstantially free of SiO₂.

According to a thirtieth aspect, the glass of any one of aspects 21-29,wherein the glass has logarithm of liquidus viscosity, Log(η_(liq), [P])that is greater than or equal to 2.0.

According to a thirty-first aspect, the glass of any one of aspects21-30, wherein the glass has one or more of the following attributes: amass difference per unit area in HCl according to DIN12116,HCl[DIN12116], that is less than or equal to 10 mg/cm² and a massdifference per unit area in NaOH according to ISO695, NaOH[IS0695], thatis less than or equal to 100 mg/cm².

According to a thirty-second aspect, the glass of any one of aspects21-31, wherein the glass has a vHF mass difference per unit area that isless than or equal to 1.0 mg/cm² and wherein the glass exhibits nosurface damage after test, as observed by a naked eye.

According to a thirty-third aspect, the glass of any one of aspects 21,23-26 or 29-32, wherein the composition of the components comprisesgreater than or equal to 8.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.0 mol. % and less than or equal to14.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than orequal to 8.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 5.0 mol. % K₂O, greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % BaO, greater than or equal to 0.0 mol.% and less than or equal to 0.2 mol. % SiO₂, greater than or equal to0.0 at. % and less than or equal to 1.0 at. % F, greater than or equalto 0.5 mol. % and less than or equal to 17.0 mol. % Li₂O+Na₂O+MgO+CaO,greater than or equal to 0.5 mol. % and less than or equal to 15.0 mol.% La₂O₃+CeO₂+Ce₂O₃ and greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. % Bi₂O₃+Cu₂O+CuO and wherein the composition of thecomponents satisfies the conditions: (La₂O₃+CeO₂+Ce₂O₃)/RE_(m)O_(n)[mol. %]≥0.51, where chemical formulas mean the content of correspondingcomponents in the glass, RE_(m)O_(n) is a total sum of rare earth metaloxides.

According to a thirty-fourth aspect, the glass of any one of aspects21-33, wherein the composition of the components satisfies thecondition: P_(E)>75, where P_(E) is calculated from the glasscomposition in terms of mol. % of the components according to theFormula (II):

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II).

According to a thirty-fifth aspect, the glass of any one of aspects21-34, wherein the glass has a Young's modulus, E that is greater thanor equal to 75 GPa.

According to a thirty-sixth aspect, the glass of the thirty-fifthaspect, wherein the glass has a Young's modulus, E that is greater thanor equal to 80 GPa.

According to a thirty-seventh aspect, the glass of the thirty-sixthaspect, wherein the glass has a Young's modulus, E that is greater thanor equal to 85 GPa.

According to a thirty-eighth aspect, the glass of the thirty-seventhaspect of any of the aspects 34-37, wherein the glass has a value of theparameter P_(E)>85.

According to a thirty-ninth aspect, the glass of any one of aspects21-38, wherein the glass has an average linear thermal expansioncoefficient of glass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that isgreater than or equal to 60 K⁻¹, and less than or equal to 70 K⁻¹.

According to a fortieth aspect, the glass of the thirty-ninth aspect,wherein the glass has an average linear thermal expansion coefficient ofglass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that is greater than or equalto 63 K⁻¹, and less than or equal to 67 K⁻¹.

According to a forty-first aspect, the glass comprises a plurality ofcomponents, the glass having a composition of the components comprisinggreater than or equal to 40.0 mol. % and less than or equal to 75.0 mol.% P₂O₅, greater than or equal to 3.0 mol. % and less than or equal to30.0 mol. % Al₂O₃, greater than or equal to 0.0 mol. % and less than orequal to 20.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 15.0 mol. % ZnO, greater than or equal to 0.0 mol. %and less than or equal to 15.0 mol. % B₂O₃, greater than or equal to 0.0mol. % and less than or equal to 1.0 mol. % SiO₂, greater than or equalto 0.0 mol. % and less than or equal to 20.0 mol. % RO, greater than orequal to 0.0 at. % and less than or equal to 1.0 at. % F, greater thanor equal to 0.5 mol. % and less than or equal to 20.0 mol. %TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂, greater than or equal to 0.5 mol. %R₂O+RO+B₂O₃, greater than or equal to 0.0 mol. % and less than or equalto 28.0 mol. % R₂O+RO and may optionally contain one or more componentsselected from MnO₂, Nb₂O₅, SnO₂, Ta₂O₅, WO₃, Sc₂O₃, Pr₂O₃, PrO₂, Pr₆O₁₁,Nd₂O₃, Eu₂O₃, EuO, Gd₂O₃, GdO₂, Tb₂O₃, Dy₂O₃, Ho₂O₃, Er₂O₃, Tm₂O₃,Yb₂O₃, Lu₂O₃ and Sm₂O₃, wherein the composition of the components issubstantially free of Cu, Co, Cr and Ni, and the composition of thecomponents satisfies the condition: P_(E)>75, where P_(E) calculatedfrom the glass composition in terms of mol. % of the componentsaccording to the Formula (II):

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II)

where RO is a total sum of divalent metal oxides, R₂O is a total sum ofmonovalent metal oxides, and an asterisk (*) means multiplication.

According to a forty-second aspect, the glass of the forty-first aspect,wherein the glass has a Young's modulus, E that is greater than or equalto 75 GPa.

According to a forty-third aspect, the glass of any one of aspects41-42, wherein the glass has a Young's modulus, E that is greater thanor equal to 80 GPa.

According to a forty-fourth aspect, the glass of any one of aspects41-43, wherein P_(E)>80.

According to a forty-fifth aspect, the glass of any one of aspects41-44, wherein the composition of the components comprises greater thanor equal to 60.0 mol. % and less than or equal to 68.0 mol. % P₂O₅,greater than or equal to 15.0 mol. % and less than or equal to 20.0 mol.% Al₂O₃, greater than or equal to 0.3 mol. % and less than or equal to12.0 mol. % B₂O₃, greater than or equal to 1.0 mol. % and less than orequal to 15.0 mol. % R₂O+RO and wherein the composition of thecomponents satisfies the condition: 0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol.%]≤1.20, where R₂O is a total sum of monovalent metal oxides, and RO isa total sum of divalent metal oxides.

According to a forty-sixth aspect, the glass of any one of aspects41-44, wherein the composition of the components comprises greater thanor equal to 48.0 mol. % and less than or equal to 75.0 mol. % P₂O₅,greater than or equal to 8.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.3 mol. % and less than or equal to40.0 mol. % Alk₂O+MgO+RE_(m)O_(n), greater than or equal to 0.25 mol. %and less than or equal to 20 mol. % TiO₂+ZrO₂ and greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O+K₂O+BaO andwherein the composition of the components is substantially free of Cu,Co, Ni, Cr, V and Bi, where Alk₂O is a total sum of alkali metal oxides,and RE_(m)O_(n) is a total sum of rare earth metal oxides.

According to a forty-seventh aspect, the glass of any one of aspects41-46, wherein the glass has a batch index, I_(B) that is greater thanor equal to 0.000, where I_(B) is calculated from the glass compositionin terms of mol. % of the components according to the Formula (I):

I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅,  (I).

According to a forty-eighth aspect, the glass of any one of aspects41-47, wherein the composition of the components satisfies thecondition: −1≤min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))≤12,where RE_(m)O_(n) is a total sum of rare earth metal oxides, and R₂O isa total sum of monovalent metal oxides.

According to a forty-ninth aspect, the glass of any one of aspects 41-44or 46-48, wherein the composition of the components comprises greaterthan or equal to 50.0 mol. % and less than or equal to 70.0 mol. % P₂O₅,greater than or equal to 10.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.0 mol. % and less than or equal to15.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and less than orequal to 10.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % CeO₂, greater than or equal to 0.0 mol. %and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0mol. % and less than or equal to 10.0 mol. % Li₂O, greater than or equalto 0.0 mol. % and less than or equal to 10.0 mol. % MgO, greater than orequal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 7.5 mol. % La₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %Y₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 4.0mol. % CaO and greater than or equal to 0.0 mol. % and less than orequal to 4.0 mol. % ZrO₂.

According to a fiftieth aspect, the glass of any one of aspects 41-44 or46-49, wherein the composition of the components comprises one or moreof the following components: greater than or equal to 53.5 mol. % andless than or equal to 66.0 mol. % P₂O₅, greater than or equal to 15.5mol. % and less than or equal to 28.5 mol. % Al₂O₃, greater than orequal to 0.75 mol. % and less than or equal to 7.25 mol. % MgO, greaterthan or equal to 0.5 mol. % and less than or equal to 8.0 mol. % B₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 11.0 mol.% TiO₂, greater than or equal to 0.0 mol. % and less than or equal to9.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than orequal to 9.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 9.0 mol. % Na₂O, greater than or equal to 0.0 mol. %and less than or equal to 6.5 mol. % CeO₂, greater than or equal to 0.0mol. % and less than or equal to 5.5 mol. % La₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 5.5 mol. % Y₂O₃, greater than orequal to 0.0 mol. % and less than or equal to 4.0 mol. % CaO, greaterthan or equal to 0.0 mol. % and less than or equal to 3.6 mol. % ZrO₂and greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % Nd₂O₃.

According to a fifty-first aspect, the glass of any one of aspects 41-44or 46-50, wherein the composition of the components comprises greaterthan or equal to 58.0 mol. % and less than or equal to 66.0 mol. % P₂O₅,greater than or equal to 16.0 mol. % and less than or equal to 27.0 mol.% Al₂O₃, greater than or equal to 1.5 mol. % and less than or equal to7.8 mol. % B₂O₃, greater than or equal to 1.5 mol. % and less than orequal to 6.3 mol. % MgO, greater than or equal to 0.0 mol. % and lessthan or equal to 10.0 mol. % TiO₂, greater than or equal to 0.0 mol. %and less than or equal to 8.0 mol. % K₂O, greater than or equal to 0.0mol. % and less than or equal to 8.0 mol. % Li₂O, greater than or equalto 0.0 mol. % and less than or equal to 8.0 mol. % Na₂O, greater than orequal to 0 mol. % and less than or equal to 5.75 mol. % CeO₂, greaterthan or equal to 0 mol. % and less than or equal to 4.75 mol. % La₂O₃,greater than or equal to 0 mol. % and less than or equal to 4.75 mol. %Y₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 3.4mol. % CaO, greater than or equal to 0.0 mol. % and less than or equalto 3.2 mol. % ZrO₂ and greater than or equal to 0.0 mol. % and less thanor equal to 1.5 mol. % Nd₂O₃.

According to a fifty-second aspect, the glass of any one of aspects41-51, wherein the composition of the components comprises greater thanor equal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %BaO, greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % V₂O₅, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition ofthe components is substantially free of Cu, Co, Ni, Cr, V and Bi,substantially free of fluorine, substantially free of PbO andsubstantially free of SiO₂.

According to a fifty-third aspect, the glass of any one of aspects41-52, wherein the glass has a logarithm of liquidus viscosity,Log(η_(liq), [P]) that is greater than or equal to 2.0.

According to a fifty-fourth aspect, the glass of any one of aspects41-53, wherein the glass has one or more of the following attributes: amass difference per unit area in HCl according to DIN12116,HCl[DIN12116], that is less than or equal to 10 mg/cm² and a massdifference per unit area in NaOH according to ISO695, NaOH[IS0695], thatis less than or equal to 100 mg/cm².

According to a fifty-fifth aspect, the glass of any one of aspects41-54, wherein the glass has a vHF mass difference per unit area that isless than or equal to 1.0 mg/cm².

According to a fifty-sixth aspect, the glass of any one of aspects 41-48or 52-55, wherein the composition of the components comprises greaterthan or equal to 8.0 mol. % and less than or equal to 30.0 mol. % Al₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 14.0 mol.% Li₂O, greater than or equal to 0.0 mol. % and less than or equal to8.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and less than orequal to 5.0 mol. % K₂O, greater than or equal to 0.0 mol. % and lessthan or equal to 3.0 mol. % BaO, greater than or equal to 0.0 mol. % andless than or equal to 0.2 mol. % SiO₂, greater than or equal to 0.5 mol.% and less than or equal to 17.0 mol. % Li₂O+Na₂O+MgO+CaO, greater thanor equal to 0.5 mol. % and less than or equal to 15.0 mol. %La₂O₃+CeO₂+Ce₂O₃ and greater than or equal to 0.0 mol. % and less thanor equal to 1.0 mol. % Bi₂O₃+Cu₂O+CuO and wherein the composition of thecomponents satisfies the condition: (La₂O₃+CeO₂+Ce₂O₃)/RE_(m)O_(n) [mol.%]≥0.51, where RE_(m)O_(n) is a total sum of rare earth metal oxides.

According to a fifty-seventh aspect, the glass of any one of aspects41-56, wherein the composition of the components satisfies thecondition: P_(E)>80, where P_(E) is calculated from the glasscomposition in terms of mol. % of the components according to theFormula (II):

P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II).

According to a fifty-eighth aspect, the glass of any one of aspects41-57, wherein the glass has a Young's modulus, E that is greater thanor equal to 80 GPa.

According to a fifty-ninth aspect, the glass of the fifty-eighth aspect,wherein the glass has a Young's modulus, E that is greater than or equalto 85 GPa.

According to a sixtieth aspect, the glass of any one of aspects 41-59,wherein the glass has an average linear thermal expansion coefficient ofglass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that is greater than or equalto 60 K⁻¹, and less than or equal to 70 K⁻¹.

According to a sixty-first aspect, the glass of the sixtieth aspect,wherein the glass has an average linear thermal expansion coefficient ofglass in the range 20-300° C., α₂₀₋₃₀₀×10⁷ that is greater than or equalto 63 K⁻¹, and less than or equal to 67 K⁻¹.

Many variations and modifications may be made to the above-describedembodiments of the disclosure without departing substantially from thespirit and various principles of the disclosure. All such modificationsand variations are intended to be included herein within the scope ofthis disclosure and protected by the following claims.

To the extent not already described, the different features of thevarious aspects of the present disclosure may be used in combinationwith each other as desired. That a particular feature is not explicitlyillustrated or described with respect to each aspect of the presentdisclosure is not meant to be construed that it cannot be, but it isdone for the sake of brevity and conciseness of the description. Thus,the various features of the different aspects may be mixed and matchedas desired to form new aspects, whether or not the new aspects areexpressly disclosed.

1. A glass comprising a plurality of components, the glass having acomposition of the components comprising: greater than or equal to 0.3mol. % and less than or equal to 50.0 mol. % B₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 75.0 mol. % P₂O₅, greater thanor equal to 0.5 mol. % and less than or equal to 15.0 mol. % MgO,greater than or equal to 0.0 mol. % and less than or equal to 30.0 mol.% Al₂O₃, greater than or equal to 0.0 mol. % and less than or equal to1.0 mol. % Cu₂O+CuO, greater than or equal to 0.3 mol. % and less thanor equal to 15.0 mol. % R₂O, greater than or equal to 0.0 at. % and lessthan or equal to 0.5 at. % F, greater than or equal to 15.0 mol. % andless than or equal to 75.0 mol. % P₂O₅+B₂O₃, greater than or equal to0.8 mol. % and less than or equal to 15.0 mol. % R₂O+RO+SnO₂+MnO₂ andgreater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. %TeO₂+GeO₂, wherein the composition of the components is substantiallyfree of SiO₂ and substantially free of PbO and wherein the compositionof the components satisfies the condition:(Li₂O+Na₂O)/R₂O [mol. %]≥0.75, where R₂O is a total sum of monovalentmetal oxides, and RO is a total sum of divalent metal oxides.
 2. Theglass of claim 1, wherein the composition of the components comprises:greater than or equal to 60.0 mol. % and less than or equal to 68.0 mol.% P₂O₅, greater than or equal to 15.0 mol. % and less than or equal to20.0 mol. % Al₂O₃, greater than or equal to 0.3 mol. % and less than orequal to 12.0 mol. % B₂O₃, greater than or equal to 1.0 mol. % and lessthan or equal to 15.0 mol. % R₂O+RO and wherein the composition of thecomponents satisfies the condition:0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol. %]≤1.20.
 3. The glass of claim 1, whereinthe composition of the components has a batch index, I_(B) that isgreater than or equal to 0.000, where I_(B) is calculated from the glasscomposition in terms of mol. % of the components according to thefollowing formula:I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅.
 4. The glass of claim 1,wherein the composition of the components comprises one or more of thefollowing: greater than or equal to 53.5 mol. % and less than or equalto 66.0 mol. % P₂O₅, greater than or equal to 15.5 mol. % and less thanor equal to 28.5 mol. % Al₂O₃, greater than or equal to 0.75 mol. % andless than or equal to 7.25 mol. % MgO, greater than or equal to 0.5 mol.% and less than or equal to 8.0 mol. % B₂O₃, greater than or equal to0.0 mol. % and less than or equal to 11.0 mol. % TiO₂, greater than orequal to 0.0 mol. % and less than or equal to 9.0 mol. % K₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 9.0 mol. % K₂O,greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5mol. % CeO₂, greater than or equal to 0.0 mol. % and less than or equalto 5.5 mol. % La₂O₃, greater than or equal to 0.0 mol. % and less thanor equal to 5.5 mol. % Y₂O₃, greater than or equal to 0.0 mol. % andless than or equal to 4.0 mol. % CaO, greater than or equal to 0.0 mol.% and less than or equal to 3.6 mol. % ZrO₂ and greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. % Nd₂O₃.
 5. The glass ofclaim 1, wherein the composition of the components comprises: greaterthan or equal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %BaO, greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % V₂O₅, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition ofthe components is substantially free of Cu, Co, Ni, Cr, V and Bi andsubstantially free of fluorine.
 6. The glass of claim 1, wherein theglass has a vHF mass difference per unit area that is less than or equalto 1.0 mg/cm².
 7. The glass of claim 1, wherein the glass satisfies thecondition:P _(E)>75, where P_(E) is calculated from the glass composition in termsof mol. % of the components according to the Formula (II):P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II).8. A glass comprising a plurality of components, the glass having acomposition of the components comprising greater than or equal to 40.0mol. % and less than or equal to 75.0 mol. % P₂O₅, greater than or equalto 0.5 mol. % and less than or equal to 10.5 mol. % B₂O₃, greater thanor equal to 0.0 mol. % and less than or equal to 25.0 mol. % Al₂O₃,greater than or equal to 0.0 mol. % and less than or equal to 0.5 mol. %SiO₂, greater than or equal to 0.0 at. % and less than or equal to 5.0at. % F, greater than or equal to 0.5 mol. % R₂O+RO, greater than orequal to 0.0 mol. % and less than or equal to 9.5 mol. % K₂O+Rb₂O+Cs₂Oand greater than or equal to 0.0 mol. % and less than or equal to 0.5mol. % ZnO+CuO+Cu₂O, wherein the composition of components satisfies theconditions:3*Al₂O₃+R₂O+RO−P₂O₅ [mol. %]≥−7.0 andAl₂O₃−R₂O−RO [mol. %]≥7.95.
 9. The glass of claim 8, wherein thecomposition of the components comprises: greater than or equal to 60.0mol. % and less than or equal to 68.0 mol. % P₂O₅, greater than or equalto 15.0 mol. % and less than or equal to 20.0 mol. % Al₂O₃, greater thanor equal to 0.5 mol. % and less than or equal to 12.0 mol. % B₂O₃,greater than or equal to 1.0 mol. % and less than or equal to 15.0 mol.% R₂O+RO and wherein the composition of the components satisfies thecondition:0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol. %]≤1.20, where R₂O is a total sum ofmonovalent metal oxides, and RO is a total sum of divalent metal oxides.10. The glass of claim 8, wherein the glass has batch index, I_(B) thatis greater than or equal to 0.000 where I_(B) is calculated from theglass composition in terms of mol. % of the components according to thefollowing formula:I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅.
 11. The glass of claim 8,wherein the composition of the components comprises one or more of thefollowing: greater than or equal to 53.5 mol. % and less than or equalto 66.0 mol. % P₂O₅, greater than or equal to 15.5 mol. % and less thanor equal to 28.5 mol. % Al₂O₃, greater than or equal to 0.75 mol. % andless than or equal to 7.25 mol. % MgO, greater than or equal to 0.5 mol.% and less than or equal to 8.0 mol. % B₂O₃, greater than or equal to0.0 mol. % and less than or equal to 11.0 mol. % TiO₂, greater than orequal to 0.0 mol. % and less than or equal to 9.0 mol. % K₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 9.0 mol. % Li₂O,greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5mol. % CeO₂, greater than or equal to 0.0 mol. % and less than or equalto 5.5 mol. % La₂O₃, greater than or equal to 0.0 mol. % and less thanor equal to 5.5 mol. % Y₂O₃, greater than or equal to 0.0 mol. % andless than or equal to 4.0 mol. % CaO, greater than or equal to 0.0 mol.% and less than or equal to 3.6 mol. % ZrO₂ and greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. % Nd₂O₃.
 12. The glass ofclaim 8, wherein the composition of the components comprises: greaterthan or equal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %BaO, greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % V₂O₅, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition ofthe components is substantially free of Cu, Co, Ni, Cr, V and Bi,substantially free of fluorine, substantially free of PbO andsubstantially free of SiO₂.
 13. The glass of claim 8, wherein the glasshas a vHF mass difference per unit area that is less than or equal to1.0 mg/cm².
 14. The glass of claim 8, wherein the glass satisfies theconditions: P_(E)>75, where P_(E) is calculated from the glasscomposition in terms of mol. % of the components according to theFormula (II):P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II).15. A glass comprising a plurality of components, the glass having acomposition of the components comprising: greater than or equal to 40.0mol. % and less than or equal to 75.0 mol. % P₂O₅, greater than or equalto 3.0 mol. % and less than or equal to 30.0 mol. % Al₂O₃, greater thanor equal to 0.0 mol. % and less than or equal to 20.0 mol. % Li₂O,greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol.% ZnO, greater than or equal to 0.0 mol. % and less than or equal to15.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than orequal to 1.0 mol. % SiO₂, greater than or equal to 0.0 mol. % and lessthan or equal to 20.0 mol. % RO, greater than or equal to 0.0 at. % andless than or equal to 1.0 at. % F, greater than or equal to 0.5 mol. %and less than or equal to 20.0 mol. % TiO₂+La₂O₃+Y₂O₃+Ce₂O₃+CeO₂+ZrO₂,greater than or equal to 0.5 mol. % R₂O+RO+B₂O₃, greater than or equalto 0.0 mol. % and less than or equal to 28.0 mol. % R₂O+RO andoptionally comprising one or more components selected from MnO₂, Nb₂O₅,SnO₂, Ta₂O₅, WO₃, Sc₂O₃, Pr₂O₃, PrO₂, Pr₆O₁₁, Nd₂O₃, Eu₂O₃, EuO, Gd₂O₃,GdO₂, Tb₂O₃, Dy₂O₃, Ho₂O₃, Er₂O₃, Tm₂O₃, Yb₂O₃, Lu₂O₃ and Sm₂O₃, whereinthe composition of the components is substantially free of Cu, Co, Crand Ni, and wherein the glass satisfies the conditions:P _(E)>75, where P_(E) is calculated from the glass composition in termsof mol. % of the components according to the Formula (II):P_(E)=−0.27146*P₂O₅+0.96062*Al₂O₃+0.22431*B₂O₃−0.072878*BaO+0.35074*CaO+0.21526*(Ce₂O₃+CeO₂)−0.12628*Cu₂O−0.5807*K₂O+0.41579*La₂O₃+0.18714*Li₂O+0.20336*MgO+0.061862*MnO−0.057105*MnO₂−0.18615*Na₂O+0.64778*Nb₂O₅−0.35317*PbO−0.028357*SiO₂+0.17429*SnO+0.55551*SnO₂+0.8294*Ta₂O₅+0.60217*TiO₂+0.17356*WO₃+0.36256*Y₂O₃−0.19958*ZnO+0.7835*ZrO₂+0.46259*(RE_(m)O_(n)−La₂O₃−Y₂O₃−Ce₂O₃−CeO₂)+0.90549*(max(0,min(B₂O₃,P₂O₅−(3*Al₂O₃+3*RE_(m)O_(n)+R₂O+MgO+CaO))))+70,  (II)where RO is a total sum of divalent metal oxides and R₂O is a total sumof monovalent metal oxides.
 16. The glass of claim 15, wherein the glasshas a Young's modulus, E that is greater than or equal to 75 GPa. 17.The glass of claim 15, wherein the composition of the componentscomprises: greater than or equal to 60.0 mol. % and less than or equalto 68.0 mol. % P₂O₅, greater than or equal to 15.0 mol. % and less thanor equal to 20.0 mol. % Al₂O₃, greater than or equal to 0.3 mol. % andless than or equal to 12.0 mol. % B₂O₃, greater than or equal to 1.0mol. % and less than or equal to 15.0 mol. % R₂O+RO and wherein thecomposition of the components satisfies the condition:0.95≤P₂O₅/(3*Al₂O₃+B₂O₃) [mol. %]≤1.20, where R₂O is a total sum ofmonovalent metal oxides and RO is a total sum of divalent metal oxides.18. The glass of claim 15, wherein the glass has batch index, I_(B) thatis greater than or equal to 0.000 where I_(B) is calculated from theglass composition in terms of mol. % of the components according to thefollowing formula:I _(B)=(R₂O+RO+3*Al₂O₃+B₂O₃+3*RE₂O₃)−P₂O₅.
 19. The glass of claim 15,wherein the composition of the components comprises one or more of thefollowing: greater than or equal to 53.5 mol. % and less than or equalto 66.0 mol. % P₂O₅, greater than or equal to 15.5 mol. % and less thanor equal to 28.5 mol. % Al₂O₃, greater than or equal to 0.75 mol. % andless than or equal to 7.25 mol. % MgO, greater than or equal to 0.5 mol.% and less than or equal to 8.0 mol. % B₂O₃, greater than or equal to0.0 mol. % and less than or equal to 11.0 mol. % TiO₂, greater than orequal to 0.0 mol. % and less than or equal to 9.0 mol. % K₂O, greaterthan or equal to 0.0 mol. % and less than or equal to 9.0 mol. % Li₂O,greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5mol. % CeO₂, greater than or equal to 0.0 mol. % and less than or equalto 5.5 mol. % La₂O₃, greater than or equal to 0.0 mol. % and less thanor equal to 5.5 mol. % Y₂O₃, greater than or equal to 0.0 mol. % andless than or equal to 4.0 mol. % CaO, greater than or equal to 0.0 mol.% and less than or equal to 3.6 mol. % ZrO₂ and greater than or equal to0.0 mol. % and less than or equal to 1.0 mol. % Nd₂O₃.
 20. The glass ofclaim 15, wherein the composition of the components comprises: greaterthan or equal to 0.0 mol. % and less than or equal to 5.0 mol. % Ta₂O₅,greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %BaO, greater than or equal to 0.0 mol. % and less than or equal to 1.0mol. % V₂O₅, greater than or equal to 0.0 mol. % and less than or equalto 3.0 mol. % K₂O+Rb₂O+Cs₂O and greater than or equal to 0.0 mol. % andless than or equal to 3.0 mol. % TeO₂+GeO₂, wherein the composition ofthe components is substantially free of Cu, Co, Ni, Cr, V and Bi,substantially free of fluorine, substantially free of PbO andsubstantially free of SiO₂.
 21. The glass of claim 15, wherein the glasshas a vHF mass difference per unit area that is less than or equal to1.0 mg/cm².